WO2018151297A1 - Method for designing rolled h-shaped steel, rolled h-shaped steel, and method for manufacturing rolled h-shaped steel - Google Patents

Abstract

In this method for designing rolled H-shaped steel, where a value obtained by dividing the cross-sectional secondary moment Ix about a strong axis by the outer circumferential length Lp of a cross-sectional shape, when viewed in a vertical cross-section in the material axis direction, is defined as surface treatment economic efficiency Ix/Lp, and the area of the cross-sectional shape is defined as S, the following are set so as to satisfy a prescribed relational expression: the height dimension H from an upper flange to a lower flange; the width dimension W of each of the upper flange and lower flange; the thickness tw of a web; and the thickness tf of each of the upper flange and lower flange.

Description

Rolled H-section steel design method, rolled H-section steel, and rolled H-section steel manufacturing method

The present invention relates to a design method for rolled H-section steel, rolled H-section steel, and a method for manufacturing rolled H-section steel.
This application claims priority based on Japanese Patent Application No. 2017-028465 filed in Japan on February 17, 2017, the contents of which are incorporated herein by reference.

For the purpose of providing an economical and reliable structural system for deformably resisting a temporary load caused by an earthquake or an impact or other severe temporary cause, Patent Document 1 discloses a steel beam. Is disclosed.

In the steel beam disclosed in Patent Document 1, the deformation capability is enhanced by using a large number of distributed regions determined by one or more voids arranged in the web of the support member that becomes the steel beam. This void is of a size, shape and configuration that ensures that the dispersive region is inelastically deformed when reaching critical stress, allowing mechanical equipment, wires, etc. to pass through the void.

Japanese Laid-Open Patent Publication No. 2008-175056

Here, the steel beam disclosed in Patent Document 1 is formed in the web when, for example, the outer peripheral surface of the web is coated or painted because a void is formed in the web of the support member that becomes the steel beam. The amount of web coating, the amount of fireproof coating, the amount of plating, etc. can be reduced by the amount of space created.

However, in the steel beam disclosed in Patent Document 1, since a void is formed in the web of the support member that becomes the steel beam, a cross-sectional defect occurs in the void portion in the web. Stiffness decreases. Therefore, in the steel beam disclosed in Patent Document 1, there is a problem in that a local fracture phenomenon due to local buckling, shear buckling, clip ring buckling, or the like is likely to occur in the web of the support member that becomes the steel beam. there were.

The present invention has been made in view of the above circumstances, and is a rolled H-shape capable of reducing the cost for surface treatment such as coating or painting while suppressing local destruction phenomenon due to local buckling. It aims at providing the design method of steel, the rolling H-section steel, and the manufacturing method of rolling H-section steel.

The present invention employs the following in order to solve the above problems.
(1) The design method of the rolled H-section steel according to the first aspect of the present invention includes an upper flange and a lower flange, a web connecting the upper flange and the lower flange, and the upper flange and the lower flange. This is a method of designing a rolled H-section steel whose surface is treated with the flange and the outer peripheral surface of the web, and the outer peripheral length Lp in the cross-sectional shape when viewed in a cross section perpendicular to the material axis direction. When the value obtained by dividing the next moment Ix is the surface treatment economy Ix / Lp, and the area of the cross-sectional shape is S, the following expressions (35) to (38) are satisfied, and the upper flange to the lower flange are satisfied. The height dimension H is 700 mm or more, the width dimension W of each of the upper flange and the lower flange is 1/5 or more and 1/2 or less of the height dimension H, and the thickness tw of the web 9mm or more 3 The height dimension H, the width dimension W, the sheet thickness tw, and the sheet thickness tf are set so that the thickness tf of each of the upper flange and the lower flange is 12 mm or more and 40 mm or less. Set.
(2) In the aspect described in (1) above, the rolling H-section steel may be configured as follows: the rolled H-section steel is used as a beam extending in the material axis direction, and the rolling shaft of the rolled H-section steel A condition in which both ends in the direction are fixed, a condition in which lateral movement in the width direction of the rolled H-section steel is restrained in the intermediate part in the material axis direction, and an intermediate load acts on the upper flange from above and Under the condition that end loads are applied to both ends in the material axis direction, the beam is laterally _buckled using the elastic lateral buckling moment M _cr of the beam calculated from the following equations (12) to (16). The height dimension H, the width dimension W, the plate thickness tw, and the plate thickness tf are set so as not to occur.
However, V _cr : Shear force acting on the end of the beam in the material axis direction, W _cr : Intermediate load acting on the intermediate portion of the beam in the material axis direction, β and γ: Loads V _cr and W _cr ) And coefficients determined from the formula (2), l: length of the beam in the axial direction, E: Young's modulus, I: secondary moment of inertia around the weak axis of the lower flange, G: shear modulus, J: sun · torsional constant of safe, d _b: plate thickness center distance between the upper and lower flanges, y: from one end thereof in a timber axis direction of the reference beam to any point of the timber axis direction of the beam length, theta _y: Lateral torsion angle caused in the beam by bending, θ _'y: the first derivative of θ _y, θ _"y: second differential of θ _y, a: a parametric for integration.
(3) In the aspect described in the above (2), as the square root of the total plastic moment Mp of the rolled H-shaped steel the elastic Lateral Buckling moment M _cr divided by is 0.6 or less, the height The dimension H, the width dimension W, the plate thickness tw, and the plate thickness tf may be set.

(4) The rolled H-section steel according to the second aspect of the present invention is a rolled H-section steel comprising an upper flange and a lower flange; and a web connecting the upper flange and the lower flange. The lower flange and the outer peripheral surface of the web are surface-treated; the height dimension H from the upper flange to the lower flange is 700 mm or more; and the width dimension W of each of the upper flange and the lower flange is 1/5 or more and 1/2 or less of the height dimension H; the plate thickness tw of the web is 9 mm or more and 32 mm or less; and the plate thickness tf of each of the upper flange and the lower flange is 12 mm or more and 40 mm or less. Yes; the value obtained by dividing the cross-sectional secondary moment Ix around the strong axis by the outer peripheral length Lp in the cross-sectional shape when viewed in a cross section perpendicular to the material axis direction is the surface treatment economic Ix / Lp, When the area of the surface shape and S, the height H, the width W, the thickness tw, and the thickness tf satisfies the equation (35) to (38) below.

(5) A method for producing a rolled H-section steel according to the third aspect of the present invention is the high H set by the method for designing a rolled H-section steel according to any one of (1) to (3) above. The rolled H-section steel having a thickness H, the width W, the plate thickness tw, and the plate thickness tf is manufactured.

According to each of the above aspects of the present invention, it is possible to reduce the cost for surface treatment such as coating or painting while suppressing local destruction phenomenon due to local buckling.

It is a perspective view which shows the rolling H-section steel which concerns on one Embodiment of this invention. It is a front view which shows the said rolled H-section steel. It is a side view which shows the said rolled H-section steel. It is an enlarged front view which shows the surface treatment economical efficiency of the said rolled H-section steel. It is a graph which shows the relationship between surface treatment economical efficiency Ix / Lp in conventional H-section steel, and H / S. In the conventional H-section steel, it is a graph which shows that the relationship between surface treatment economics Ix / Lp and H / S becomes “Ix / Lp <730 · exp (−45 · H / S)”. In the rolled H-section steel according to an embodiment of the present invention, the relationship between the surface treatment economics Ix / Lp and H / S is “Ix / Lp ≧ 730 · exp (−45 · H / S)”. It is a graph which shows. In the rolled H-section steel, the relationship between the cross-sectional area S and the height dimension H is “0.015 ≦ H / S ≦ 0.065”. It is a front view of the beam using the said rolling H-section steel, Comprising: It is a figure which shows the state by which both ends were fixed and lateral movement was restrained. It is a side view of the state shown to FIG. 8A. It is a side view which shows an example of the virtual displacement of the beam using the said rolled H-section steel. It is a bottom view which shows the virtual displacement of the beam shown to FIG. 9A. FIG. 9B is a sectional view taken along line AA ′ of FIG. 9A. It is a graph which compares transition of the shape of a beam, steel material weight, and holding performance in the conventional design method and the design method of the present invention. It is a schematic side view which shows the equal bending moment in case the intermediate load becomes equal bending in the beam using the rolled H-section steel which concerns on one Embodiment of this invention. It is a schematic side view which shows an example of a reverse symmetric moment etc. when an intermediate load does not become equal bending in the beam using the said rolled H-section steel. It is a schematic side view which shows other examples, such as a reverse symmetric moment, when an intermediate load does not become equal bending in the beam in which the said rolled H-section steel was used. It is a schematic side view which shows other examples, such as a reverse symmetric moment, when an intermediate load does not become equal bending in the beam in which the said rolled H-section steel was used. It is a graph which shows the calculation result using (theta) _y approximated by a predetermined series in the beam in which the said rolled H-section steel was used. It is a graph which shows the calculation result using (theta) _y approximated by a Fourier series in the beam in which the said rolled H-section steel was used. It is a schematic side view which shows the moment gradient used for evaluation of the Example of the said rolled H-section steel. 3 is a graph showing various rolled H-section steels (examples of the present invention) that satisfy the following expressions (35) to (38) and conventional rolled H-section steels that do not satisfy these expressions.

Hereinafter, a rolled H-section steel 1 (hereinafter also simply referred to as “H-section steel 1”) according to an embodiment of the present invention will be described with reference to the drawings. In the present specification and the drawings, the same reference numerals are given to components having substantially the same functional configuration, and a duplicate description thereof is omitted.

As shown in FIG. 1, the H-section steel 1 is mainly used in buildings such as houses, schools, offices, hospital facilities, low-rise buildings, high-rise buildings, or high-rise buildings. It becomes a structural material such as a structure.
The H-section steel 1 is a rolled H-section steel (rolled H-section steel) formed from a single steel sheet by hot rolling or the like. That is, in the H-section steel 1, the upper flange 21, the lower flange 22, and the web 23 are integrally formed.
In addition, the built-in H-section steel manufactured by welding a plurality of steel plates (the built-in H-section steel in which the upper flange 21, the lower flange 22, and the web 23 are manufactured as separate steel plates and welded to each other) However, when a fatigue crack is generated due to repeated acting force on the welded portion, or when the welding assembly accuracy of the H-section steel is poor, the application accuracy of the design method may be reduced. On the other hand, in the case of rolled H-section steel, since the flange and web are integrated (because there are no joints), the occurrence of fatigue cracks is not expected and the dimensional accuracy is high, so the application of the design method High accuracy is maintained. From such a viewpoint, the present invention is directed to rolled H-section steel.

The H-section steel 1 is used as a beam 2 extending in the material axis direction Y (longitudinal direction of the H-section steel 1) like a steel beam in a building, for example. As shown in FIGS. 2A and 2B, the H-section steel 1 has a substantially H-shaped cross-section when viewed in a cross section perpendicular to the material axis direction Y (cross-sectional shape of a cross section perpendicular to the material axis direction Y). The upper flange 21 and the lower flange 22 extending in the width direction X, and the web 23 extending in the height direction Z are provided.

As shown in FIG. 2A, the H-section steel 1 is provided with a pair of upper and lower upper flanges 21 and 22, and a web 23 is connected to the upper flange 21 and the lower flange 22. That is, in the H-section steel 1, the upper and lower ends of the web 23 are connected to substantially the center in the width direction X of the upper flange 21 and the lower flange 22 that face each other.

As shown in FIG. 2B, the entire H-section steel 1 extends in the material axis direction Y and has a predetermined length l. In the H-section steel 1, the distance in the height direction Z from the center of the plate thickness of the upper flange 21 to the center of the plate thickness of the lower flange 22 is the distance d between the plate thickness centers of the upper flange 21 and the lower flange 22. _b .

Incidentally, the distance d _b between the thickness center distance in the height direction Z from the upper surface of the upper flange 21 to the upper surface of the lower flange 22, or from the lower surface of the upper flange 21 and the lower surface of the lower flange 22 in the height direction Z It can also be handled as the same as the distance. Further, the distance d _b between the plate thickness centers is substantially the same as the distance in the height direction Z from the lower surface of the upper flange 21 to the upper surface of the lower flange 22 or the overall height dimension H of the H-section steel 1. It can also be handled.

As shown in FIG. 3, the H-section steel 1 is formed such that the upper flange 21 and the lower flange 22 extend in the width direction X, and the web 23 extends in the height direction Z. The H-section steel 1 has a strong axis that passes through the centroid (a point (center of gravity) where the primary moment of inertia with respect to an arbitrary axis passing through the point becomes zero) and extends in the width direction X, and passes through the centroid and in the height direction Z. It has two main axes with a weak axis extending in the direction. A cross-sectional secondary moment around the strong axis is defined as Ix, and a cross-sectional secondary moment around the weak axis is defined as Iy.

In the H-section steel 1, for example, a fire-resistant coating material is attached, wound or sprayed on the outer peripheral surface 20 (the surface of the H-section steel 1) of the upper flange 21, the lower flange 22 and the web 23. Surface treatment such as coating or plating is performed. That is, in the H-section steel 1, a surface treatment material such as a coating material, a paint, or plating is provided on the outer peripheral surface 20. In addition, as for the H-section steel 1, surface treatment may be given to all the outer peripheral surfaces 20 of the upper flange 21, the lower flange 22, and the web 23, and a part of outer peripheral surface 20 is surface-treated. Also good.

In the H-section steel 1, the total in cross-sectional shape including the upper and lower surfaces 21 a and both left and right end surfaces 21 b of the upper flange 21, the upper and lower surfaces 22 a and left and right end surfaces 22 b of the lower flange 22, and the left and right side surfaces 23 a of the web 23. The extension is defined as the outer peripheral length Lp in the cross-sectional shapes of the upper flange 21, the lower flange 22 and the web 23. And as for H-section steel 1, when this outer periphery length Lp becomes large, the usage-amount (use amount of surface treatment material), such as a fireproof coating material, a coating material, or plating, will also become large.
In the H-section steel 1 in which the web and the flange are integrally formed, curved connection portions 23b called fillets exist at the junction points (four locations) between the web 23, the upper flange 21 and the lower flange 22. . When calculating the outer peripheral length Lp, the fillet 23b (curve connecting portion) may be taken into consideration. For example, in the H-section steel 1 represented by H1000 × W350 × tw12 × tf19, the outer peripheral length Lp is 3345 mm when it is calculated assuming that one fillet is a quarter circle with a curvature radius of 18 mm. On the other hand, in the same H-section steel, when there is no fillet, that is, when there is no curved connecting portion and the web and the flange are connected at a right angle, the outer peripheral length Lp is calculated as 3376 mm. Thus, the difference between the two types of outer peripheral lengths Lp calculated based on the presence or absence of the fillet is about 1%, and it can be seen that the influence of the presence or absence of the fillet on the calculation result is sufficiently small. The curvature radius of the fillet is generally in the range of about 12 mm to 20 mm in the subject rolled H-section steel, but in the following description, the curvature radius of the fillet is assumed to be 18 mm.
Here, the above-mentioned “H-shaped steel 1 represented by H1000 × W350 × tw12 × t19” means that a height dimension H, a width dimension W, a web plate thickness tw, and a flange plate thickness tf, which will be described later, The H-section steel 1 which is 1000 mm, 350 mm, 12 mm, and 19 mm is pointed out. The same applies to the following description.

The H-shaped steel 1 has a height dimension H from the upper flange 21 to the lower flange 22 (a distance in the height direction Z from the upper surface of the upper flange 21 to the lower surface of the lower flange 22) of 700 mm or more.

In the H-section steel 1, the distance in the width direction X between the left and right end faces 21b of the upper flange 21 and the distance in the width direction X between the left and right end faces 22b of the lower flange 22 are respectively set as the width dimension W of the upper flange 21. , And the width dimension W of the lower flange 22, which is 1/5 or more and 1/2 or less of the height dimension H.

In the H-section steel 1, each of the upper flange 21 and the lower flange 22 has a predetermined plate thickness tf (a distance between the upper and lower surfaces 21a or a distance between the upper and lower surfaces 22a in the height direction Z), and the web 23 is It has a predetermined thickness tw (distance between the left and right side surfaces 23a in the width direction X). In addition, the ratio of the plate thickness tf to the plate thickness tw is set to a plate thickness ratio tw / tf.
In the H-section steel 1, the plate thickness tw of the web 23 is 9 mm or more and 32 mm or less, and the plate thickness tf of the upper flange 21 and the lower flange 22 is 12 mm or more and 40 mm or less.

Here, for example, when the H-section steel 1 is used as the beam 2 shown in FIG. 1, it is required to improve the bending rigidity in the height direction Z in order to suppress the deflection in the height direction Z. The H-section steel 1 can be bent per unit weight by increasing the height dimension H (by extending the H-section steel in the height direction) to increase the cross-sectional secondary moment Ix around the strong axis. The bending rigidity in the height direction Z of the H-section steel 1 can be improved by improving the rigidity.

Further, in the H-section steel 1, when the outer peripheral length Lp in the cross-sectional shapes of the upper flange 21, the lower flange 22, and the web 23 is increased, the surface area of the outer peripheral surface 20 on which surface treatment such as coating is performed also increases. In this case, the amount of use of a surface treatment material such as a fireproof coating material, paint or plating is increased, and the amount of work such as painting is also increased, thereby increasing the cost required for the surface treatment.
Therefore, it is required to reduce the surface treatment cost by reducing the outer peripheral length Lp to reduce the surface area of the outer peripheral surface 20.

In general, for example, an outer-method constant H-section steel (H-section steel represented by H900 × W400 × tw19 × tf28) defined in JIS G 3192 has a steel weight per meter of about 304 kg / m, The surface area per meter is about 3.36 m ² . Further, for example, when the outer peripheral surface of the outer-method constant H-shaped steel is coated with an expensive fire-resistant paint or cold-resistant paint, the material unit price is, for example, 10,000 yen / m ² .
Therefore, assuming that the unit price of the H-shape steel with constant outer method is 120,000 yen / ton, the steel material cost in the beam 2 having a length of 10 m in the material axis direction Y is about 36,000 yen (120,000 yen / ton). × 0.304 ton / m × 10 m), while the coating material cost is about 336,000 yen (10,000 yen / m ² × 3.36 m ² / m × 10 m). That is, by comparing the cost of steel materials and the cost of coating materials, in order to reduce the total cost of buildings, etc., not only the steel weight of the H-section steel 1 but also the surface area of the outer peripheral surface 20 should be reduced in a balanced manner. It is understood that is necessary.

For this reason, in the H-section steel 1, the surface treatment economic efficiency Ix / Lp, which is a value obtained by dividing the section secondary moment Ix around the strong axis by the outer peripheral length Lp in the shape of the section perpendicular to the material axis direction Y, is an index. And When this surface treatment economy Ix / Lp is increased, the cross-sectional secondary moment Ix around the strong axis becomes relatively large with respect to the outer peripheral length Lp, so that the bending rigidity per unit weight is reduced while reducing the surface treatment cost. Can be improved.

And as for H-section steel 1, height dimension H mentioned above, width dimension W, web board thickness tw, and flange board thickness tf are determined based on surface treatment economical efficiency Ix / Lp.

As described above, the H-section steel 1 has a height dimension H, a width dimension W, a web sheet thickness tw, and a flange sheet thickness tf determined on the basis of the surface treatment economics Ix / Lp. The surface treatment cost can be reduced while increasing the sectional moment of inertia Ix.

Specifically, as described above, in the H-section steel 1, the height dimension H is 700 mm or more, the width dimension W is 1/5 or more and 1/2 or less of the height dimension H, and the web 23 The plate thickness tw is 9 mm or more and 32 mm or less, and the plate thickness tf of the flange is 12 mm or more and 40 mm or less.
Furthermore, the cross-sectional area in the cross-sectional shape of the H-section steel 1 is S (the cross-sectional areas of the upper flange 21, the lower flange 22 and the web 23 when the H-section steel 1 is viewed in a cross section perpendicular to the material axis direction Y). And the H-section steel 1 has the above-mentioned surface treatment economics Ix / Lp according to the following formulas (35) to (38). Satisfy the specified relationship. In other words, in the H-section steel 1, the height dimension H, the width dimension W, the sheet thickness tw, and the sheet thickness tf satisfy the following expressions (35) to (38). As a result, the surface treatment cost can be reduced, and at the same time, the bending rigidity per unit weight can be improved, and excessive bending deformation in the height direction Z in the H-section steel 1 can be suppressed.

The important performance indices of the H-section steel 1 are the secondary moment Ix around the strong axis, which is a structural index governing bending rigidity, and the section modulus Zx around the strong axis, which is a structural index governing bending strength. The steel material weight (cross-sectional area S), which is an economic index, and the outer peripheral length Lp, which is also an economic index. At this time, if the cross-sectional moment Ix around the large strong axis can be exhibited with the smallest outer peripheral length Lp as much as possible, it can be said that the economy is high. Therefore, in FIGS. 4 to 7, the vertical axis represents the surface treatment economy Ix / Lp. It is said. The section modulus Zx is expressed as a function of the section moment of inertia Ix around the strong axis and the height dimension H of the H-section steel 1, that is, Zx = Ix / (H / 2). The dimension H is used as a structural index, and in FIGS. 4 to 7, the horizontal axis is H / S obtained by dividing the dimension H by the cross-sectional area S that is an economic index.

Here, all of the existing standards are shown for the conventional H-section steel in FIGS. 4 to 7 as △, ◇, □, and ○ marks, respectively.
A triangle represents a conventional H-section steel indicated in “ASTM A6 / A6M-10a Annex A2 lists the dimensions of some shape profiles, ASTM International”.
The ◇ marks are conventional H-section steels shown in “BS 4-1 Structural steel sections, Part 1, British Standard, (2005)”.
The □ mark is a conventional H-section steel shown in “Constant H-section Steel, JIS Handbook, Steel II, Japanese Standards Association, (2015)”.
A circle indicates a conventional H-section steel shown in “Constant H-section steel, JIS Handbook, Steel II, Japanese Standards Association, (2015)”.

As shown in FIG. 5, these conventional H-section steels are enveloped in the range of k <6.1 in the above formulas (35) to (37). That is, it was found that these conventional H-section steels did not satisfy k ≧ 6.1 in the above formulas (35) to (37) based on the surface treatment economics Ix / Lp. On the other hand, the H-section steel 1 according to the present embodiment considers the above formulas (35) to (37) based on the surface treatment economics Ix / Lp, so that the structural index and the economic index are simultaneously obtained. Can be considered.

Specifically, in the prior art, it has been required to increase the bending rigidity while suppressing the surface treatment cost, but in the conventional design method (design method not using equation (12) described later), it is shown in FIG. Thus, k could not be over 6.0. The reason is that when the above requirements are satisfied, the design value of the lateral buckling strength (seismic resistance) is calculated to be lower than the actual value. This is because it is necessary and the economic efficiency is lowered. For example, for an H-section steel (H1100 × W300 × tw32 × tf40) where k≈6 (k <6), the buckling stiffening length Lb calculated by the conventional design method is 4 of H .6 times smaller (1100 × 4.6 = 5060). That is, in the category of the conventional design method, a lateral buckling stiffener must be installed every 5 m. And, in the range where k ≧ 6.1, Lb tends to become relatively smaller, so the number of buckling stiffeners also tends to increase. For this reason, k <6.1 in the prior art.

On the other hand, in the H-section steel 1 according to the present embodiment, the structural index and the economic index can be considered simultaneously by setting k ≧ 6.1 in the above formulas (35) to (37), and the surface treatment cost At the same time, it is possible to improve the bending rigidity per unit weight. In addition, from the viewpoint of reliably reducing the surface treatment cost and at the same time improving the bending rigidity, the H-section steel 1 can be expressed as k ≧ in the above formulas (35) to (37) as shown in FIG. It is desirable that 6.2 or k ≧ 6.25, and it is more desirable that k ≧ 6.3 or k ≧ 6.4.

In addition, the H-section steel 1 avoids a decrease in yield strength due to occurrence of lateral buckling, avoids a decrease in energy absorption performance during an earthquake, and prevents the web from wavy or twisted during rolling. From this viewpoint, the width dimension W of the H-section steel 1 is set to 1/5 or more of the height dimension H, and k ≦ 8 in the above expressions (35) to (37). For example, the surface treatment economics Ix / Lp of H-section steel 1 represented by H1200 × W160 × tw7 × tf16 is relatively high, that is, the value of k in FIG. 5 is relatively large and k> 8. In this H-section steel 1, even if calculation based on the design method of the present invention described later is performed, a sufficiently high bending strength cannot be obtained (in the case of calculation under the same conditions as the examples described later, Lateral buckling occurs in a range where the bending stiffening interval Lb is shorter than about 15 times the length of H, and the design yield strength for the total plastic moment Mp obtained by the product of the total plastic section modulus Zxp around the strong axis and the steel F value The ratio drops to about 75%), and there is a risk that sufficient earthquake resistance cannot be ensured. Based on such examination, an upper limit value of k ≦ 8 is set.
For example, in the case of H-shaped steel of H1500 × W350 × tw19 × tf40, H1500 × W400 × tw22 × tf40, and H1500 × W500 × tw16 × tf36, k≈8 (and k <8), and F = 345, When calculated by the same method as in Examples described later, it can be confirmed that the lateral buckling does not occur until the buckling stiffening interval Lb exceeds 15 times H (= 1500 mm).

In addition, in FIG. 6, the Example of H-section steel 1 is enumerated and enumerated by * mark.
Here, in Example 1, the height dimension H = 1150 mm, the width dimension W = 300 mm, the web plate thickness tw = 32 mm, and the flange plate thickness tf = 40 mm, which satisfy the above expressions (35) to (38) (H1150 * W300 * tw32 * tf40).
In Example 2, the height dimension H = 1100 mm, the width dimension W = 280 mm, the web plate thickness tw = 16 mm, and the flange plate thickness tf = 30 mm, which satisfy the above expressions (35) to (38) (H1100 × W280 × tw16 × tf30).
In Example 3, the height dimension H = 1000 mm, the width dimension W = 250 mm, the web plate thickness tw = 12 mm, and the flange plate thickness tf = 16 mm, which satisfy the above expressions (35) to (38) (H1000 × W250 × tw12 × tf16).
In Example 4, the height dimension H = 950 mm, the width dimension W = 250 mm, the web plate thickness tw = 11 mm, and the flange plate thickness tf = 25 mm, which satisfy the above expressions (35) to (38) (H950 × W250 × tw11 × tf25).
In Example 5, the height dimension H = 850 mm, the width dimension W = 200 mm, the web plate thickness tw = 10 mm, and the flange plate thickness tf = 16 mm, which satisfy the above expressions (35) to (37) (H850 × W200 × tw10 × tf16).

In addition, as shown in FIG. 7, the H-section steel 1 preferably satisfies H / S ≧ 0.015 and Ix / Lp ≧ 50 in the above equation (35). When the value of H / S is less than 0.015, for example, a special ultra-thick H-shaped steel having a flange plate thickness exceeding 60 mm is used, and used for the floor structure of a building to which the present invention is applied. Because it is difficult to be done. Moreover, in such a case, H becomes as small as 500 mm or less, and it becomes a pillar use of a building.
The lower limit of Ix / Lp may be 35, for example, but if Ix / Lp is less than 50, the surface treatment economics Ix / Lp becomes too small, so that the surface treatment cost is reduced and the bending rigidity is improved. From the viewpoint of making it possible, the lower limit of Ix / Lp is preferably 50.
The upper limit of H / S is preferably 0.065 (H / S ≦ 0.065), and more preferably 0.060 (H / S ≦ 0.060).

Here, from the viewpoint of reducing the surface treatment cost and at the same time improving the bending rigidity, the height dimension H may be increased as described above (the H-shaped steel may be extended in the height direction). However, in the beam 2, as shown in FIGS. 8A, 8B, and 9A to 9C, the web 23 is deformed out of plane with respect to the construction surface in the material axis direction Y and the height direction Z. Bending occurs. And under the design method (conventional design method) of the beam 2 according to the conventional building standard method, at both ends 2a and 2a of the beam 2 where the horizontal load at the time of the earthquake acts, or at the intermediate portion 2b of the beam 2 Since it is necessary to sufficiently consider the lateral buckling generated in the beam 2 in the portion where the negative bending moment occurs, the height dimension H cannot be easily increased.

FIG. 10 is a graph of the calculation results shown in Table 1. Columns A to I in Table 1 show the cross-sectional specifications of each H-section steel. In the A row, the cross-sectional area S is shown, and in the B row, the ratio of the cross-sectional area of other H-section steels to the cross-sectional area of H900 × W400 × tw22 × tf40, which is an H-section steel as a basis for performance comparison. The outer circumferential length Lp is shown in row C, and the ratio of the outer circumferential length of other H-section steels to the outer circumferential length Lp of the basic H-section steel (H900 × W400 × tw22 × tf40) is shown in row D. Row E shows the cross-sectional secondary moment Ix around the strong axis, and row F shows the ratio of the cross-sectional secondary moments of other H-section steels to the basic cross-section secondary moment Ix of the H-section steel. The G column shows the total plastic section modulus Zxp around the strong axis, the H column shows the steel F value, and the I column shows the total plastic moment Mp obtained by the product of Zxp and F.
Here, since the cross-sectional dimensions are set so that the values of the total plastic moment Mp are substantially the same, the values in the G column and the I column are substantially the same. The column J is the design strength Mcn (calculated based on the present invention) calculated based on the design method of the present invention, which will be described later, and the column K is the total plastic moment Mp of H900 × W400 × tw22 × tf40 (in Table 1). Is the ratio of the design strength Mcn of each H-section steel to the Mpo), the L column is the design strength Mcc calculated based on the conventional design method (calculated based on the prior art), and the M column is The ratio of the design yield strength Mcc of each H-section steel to the total plastic moment Mpo is shown.

The above-mentioned conventional design method is calculated based on the calculation of the H-shaped cross section shown in the steel structure limit state design guideline and explanation of the Architectural Institute of Japan, with a yield coefficient of 1.0.
On the other hand, the design method of the present invention is calculated by replacing the derivation formula of the elastic lateral buckling moment shown in the same book with the following equation (12) and calculating the proof stress coefficient as 1.0 as in the conventional design method. is there. In addition, when the following formula (12) is used in the design method of the present invention, a case where a vertical load acts on a beam (solid line) subjected to an antisymmetric bending due to a horizontal load shown in FIG. 13 (broken line) is an object. It is calculated as.
The buckling stiffening length Lb is 20 m in any case, and the steel material F value is 325 N / mm ^{2 in} any case.

Here, the above-described conventional design method will be specifically described. In the conventional design method described above, first, around the weak axis of the H-section steel calculated based on conditions such as the cross-sectional shape of the target H-section steel, the material length, the support conditions at both ends, and the presence or absence of lateral stiffening. Using the bending rigidity, bending torsional rigidity, Saint-Benant torsional rigidity, and lateral buckling length, the elastic lateral buckling moment of the following equation (1.a) is calculated. Next, the lateral buckling slenderness ratio is calculated from the total plastic moment of the target H-section steel and the elastic lateral buckling moment. There are three types of cases depending on the magnitude relation between the value of the lateral buckling slenderness ratio and the elastic limit slenderness ratio and the plastic limit slenderness ratio described in the guidelines. In each case, the lateral buckling limit strength of the H-section steel The calculation formula is defined. The lateral buckling limit proof stress is calculated by the nominal value of each element constituting the calculation formula, but when assuming the ultimate limit state, it is necessary to consider the variation in the target member proof stress. The lateral buckling limit proof stress in the ultimate limit state is determined by introducing a proof stress coefficient which is a reliability index based on this and multiplying this by the lateral buckling limit proof stress. According to the above guidelines, the proof stress coefficient is 1.0.

In the above (1.a) type, EI _Y: weak axis bending stiffness around, EI _W: torsional bending rigidity, GJ: San safe torsional _rigidity, k _{l b:} Lateral屈長is, _{l b:} Zaicho or LATERAL Length between bending and stiffening, C _b : moment coefficient.

The cases for the lateral buckling length _k l _b are as follows.
(A) A beam in which the ends of both members are rigidly joined to the column and the middle is not laterally stiffened: _k l _b = 0.75 × l _b
(B) A beam section in which one end is rigidly joined to a column and the other end is laterally stiffened by a lateral buckling stiffener, a beam section in which both ends are laterally stiffened by a lateral buckling stiffener, and a purlin , Bending materials such as trunk edges: _k l _b = 0.75 × l _b
(C) Simple beam: _k l _b = l _b

It is as follows for the case classification moment coefficient C _b.
(A) When the bending moment changes linearly in the lateral buckling stiffening section: (b) Equation (b) below When the intermediate bending moment is maximum in the lateral buckling stiffening section: C _b = 1 .0
(C) Simple beam with no lateral buckling stiffening fulcrum in the middle:
(I) When uniformly distributed load is applied: C _b = 1.3
(Ii) When central concentrated load is applied: C _b = 1.36

M ₂ / M ₁ in the above formula (1.b) represents the bending moment ratio of both ends of the material or the lateral buckling stiffening end.
Then, the value of the abscissa屈細length ratio lambda _b, divided if the magnitude relationship between the elastic limit slenderness _e lambda _b and plastic limit slenderness ratio _p lambda _b, and, Lateral in each case屈限field strength M _{c (nominal} yield strength) Is as follows.
(A) λ _b ≦ _p λ _b : M _c = M _p
(B) _p λ _b <λ _b ≦ _e λ _b : Formula (1.c) below (c) λ _b > _e λ _b : Formula (1.d) below

Here, the lateral buckling slenderness ratio λ _b is calculated by the following equation (1.e). In the following formula (1.e), M _{p is the} total plastic moment = F _y × Z _p , F _{y is the} yield strength, and Z _{p is the} plastic section modulus.

Further, the elastic limit slenderness ratio _e λ _b is 1 / √0.6. The plastic limit slenderness ratio _p λ _b is classified as follows.
(A) When the bending moment changes linearly within the lateral buckling stiffening section: (b) When the intermediate bending moment becomes maximum within the lateral buckling stiffening section: _p λ _b = 0.3

Then, the lateral buckling limit proof stress M _cr in the ultimate limit state is obtained by the following equation (1.g).

In contrast to the above-described conventional design method, the design method of the present invention is a method of replacing the elastic lateral buckling moment calculation formula (the above formula (1.a)) shown in the same book with the following formula (12) described below. The slenderness ratio and lateral buckling limit yield strength are calculated. In addition, the yield coefficient for considering the ultimate limit state was set to 1.0 as in the conventional design method.

The horizontal axis of the graph shown in FIG. 10 indicates four types of H-section steel, and the vertical axis indicates the ratio of the cross-sectional area S (value shown in the B column of Table 1) and the ratio of the outer peripheral length (in the D column of Table 1). Value), cross-sectional secondary moment ratio around the strong axis (value shown in column F of Table 1), design yield ratio based on the design method of the present invention (value shown in column K of Table 1), and conventional design The ratios of design proof strength based on the law (values shown in column M in Table 1) can be compared.
As shown in FIG. 10, under the conventional design method, the bending dimension (secondary moment Ix around the strong axis) is increased by increasing the height dimension H relative to the width dimension W. In addition, the steel material weight (∝ cross-sectional area S) can be reduced, while the bending strength (∝ given by the product of “the section modulus Zxp around the strong axis” and “allowable bending stress degree fc” is given. It can be seen that the “allowable bending strength” tends to decrease. This is because the section modulus Zx around the strong axis is expressed as Zx = Ix / (H / 2). Therefore, if Ix is the same, Zx tends to decrease as H increases (reason 1). ) And the allowable bending stress fc need to be reduced in consideration of the lateral buckling that occurs in the beam 2, and as the height dimension H is relatively increased, lateral buckling is more likely to occur (reason 2). Is due to.

For the above reason 1, there is a case where the performance degradation can be alleviated if the height dimension H and the width dimension W of the beam 2 are set appropriately. On the other hand, since the above reason 2 cannot be solved simply by appropriately setting the height dimension H and the width dimension W of the beam 2, it is possible to prevent the allowable bending stress fc from being reduced due to the lateral buckling of the beam 2. Is the main technical issue. As a method for preventing a reduction in the allowable bending stress degree fc, a method in which a stiffening member for lateral buckling is provided on the beam 2 to reduce the buckling stiffening interval is also conceivable. However, if the stiffening member is provided on the beam 2, the cost reduction effect by reducing the surface treatment cost or the like becomes meaningless.

The H-shaped steel 1 is used as a beam 2 extending in the material axis direction Y, and as shown in FIGS. 8A and 8B, both ends 2a and 2a of the beam 2 in the material axis direction Y are rigidly joined to the column 3 and the like. Fixed. At this time, for example, when a square steel pipe or the like is used as the column 3, both end portions 2 a and 2 a of the beam 2 are rigidly joined to the column 3 by being welded to the diaphragm 30 provided on the side surface of the square steel pipe. It is fixedly supported by.

Further, when a reinforced concrete column or an unreinforced concrete column is used as the column 3, both end portions 2 a and 2 a of the beam 2 may be welded and joined to steel beams that are substantially orthogonal to each other inside the column 3. Further, both ends 2 a and 2 a of the beam 2 may be welded to a steel column extending in the height direction Z inside the column 3 when a steel reinforced concrete column is used as the column 3.

In the H-section steel 1, both ends 2a, 2a of the beam 2 in the material axis direction Y may be fixed to the column 3 or the like by semi-rigid bonding or pin bonding. The semi-rigid joint is a joint type in which the rotational movement of the beam 2 with respect to the column 3 is restricted to some extent, and the bending stress that can be transmitted between the column 3 and the beam 2 is smaller than that of a complete rigid joint. Say. The pin joint refers to a joint type that does not restrict the rotational movement of the beam 2 with respect to the column 3, and means that there is no or minimal bending stress that can be transmitted between the column 3 and the beam 2. The definitions of semi-rigid joint, pin joint and rigid joint shall conform to the European design standard (Eurocode 3, Part 1-8).

Further, the H-section steel 1 is provided with a floor slab 4 made of concrete or the like above the upper flange 21 in the intermediate portion 2b of the beam 2 in the material axis direction Y. As the floor slab 4, for example, a concrete slab having concrete as a main structure or a deck synthetic slab having a main structure of a deck plate made of concrete and steel is used.

In the H-section steel 1, one or a plurality of shear connectors 25 such as headed studs are provided on the upper surface of the upper flange 21 at predetermined intervals in the intermediate portion 2 b in the material axis direction Y of the beam 2. The shear connector 25 is provided so as to protrude upward from the upper surface of the upper flange 21 of the beam 2 and is embedded in the concrete or the like of the floor slab 4 above the upper flange 21 of the beam 2. At this time, as shown in FIG. 8A, the H-section steel 1 has a beam 2 as shown in FIG. 8A at the intermediate portion 2 b in the material axis direction Y of the beam 2 by embedding one or more shear connectors 25 in the floor slab 4. The lateral movement in the width direction X is restricted.

Further, as shown in FIG. 8B, the H-section steel 1 to which the present invention is applied is subjected to an intermediate load due to the dead weight of the floor slab 4 and the loaded load. At this time, in the H-section steel 1, in the intermediate portion 2b of the beam 2 in the material axis direction Y, an intermediate load such as an evenly distributed load acts on the upper flange 21 from above, and each column 3 is inclined by an earthquake or the like. In this case, the end load from the column 3 acts on both ends 2a, 2a of the beam 2 in the material axis direction. Further, in the H-section steel 1, a bending moment and a shearing force act on each of both end portions 2a, 2a of the beam 2 in the material axis direction Y.

Under the design method of the present invention, as shown in FIGS. 9A to 9C, both ends 2a and 2a of the beam 2 in the material axial direction Y are fixed for the beam 2 extending in the material axial direction Y. In the intermediate portion 2b of the beam 2 in the material axis direction Y, the lateral movement of the beam 2 in the width direction X is restricted, an intermediate load is applied to the upper flange 21 from above, and both ends of the beam 2 in the material axis direction 2a, under conditions that effect the end load 2a, it is possible to calculate the elastic Lateral buckling moment M _cr of the beam 2 with high accuracy.

9A to 9C, using the local coordinate system XYZ fixed at the left end 2a of the beam 2, the rotation of the beam 2 is positive in the direction in which the left screw advances. 9A to 9C, the solid line represents the free body of the beam 2, and the broken line represents an example of a virtual displacement that occurs in the free body of the beam 2 due to lateral buckling.

<Geometric boundary conditions>
The upper flange 21 of the beam 2 is assumed to be restrained from displacement (lateral movement) in the X direction on its center line 0-0 ′. The geometric boundary condition of the end 2a of the beam 2 is defined by a series of terminal conditions approximating lateral buckling deformation. The beam 2 undergoes bending torsion with 0-0 'as a predetermined rotation axis due to lateral buckling, and also bends as a secondary minor deformation. In this analysis, the upper flange 21, the lower flange 22 and the web 23 are treated as flat plates. The strength of the beam 2 against lateral buckling is determined by the bending rigidity in the plane of the upper flange 21 and the lower flange 22, the upper flange 21, and the lower flange. It is assumed that it is governed by the torsional rigidity of the flange 22 and the web 23.

<Mechanical boundary conditions>
It is assumed that a vertically evenly distributed load W _cr acts as an intermediate load on 0-0 ′ at the intermediate portion 2b of the beam 2. Further, it is assumed that a bending moment M _cr and a shearing force V _cr act on the right end 2 a of the beam 2, and a bending moment M and a shearing force V that balance these act on the left end 2 a of the beam 2. At this time, the relationship between M _cr , V _cr, and W _cr can be expressed by the following equations (1) and (2), respectively, based on the force balance condition.

Here, l is the length in the material axis direction Y of the beam 2, and y is the end of the beam 2 from one end (the left end 2 a in the case of FIG. 5) as a reference in the material axis direction of the beam 2. It is the length to an arbitrary point in the material axis direction. β and γ are coefficients determined by the load condition of the intermediate load, and are for eliminating the V _cr , W _cr , M, and V from the analytical solution and expressing them as elastic lateral buckling moments M _cr .

The relationship between the bending moment distribution of the beam 2 and β and γ is illustrated in FIGS. 11A to 11D. When the intermediate load is equal bending in the material axis direction Y of the beam 2 (symmetric buckling), β is set to zero as shown in FIG. 11A. Further, when the intermediate load is not bend in the material axis direction Y of the beam 2 (asymmetric buckling), as shown in FIGS. 11B to 11D, β is a real number greater than 0 and less than or equal to 3 (however, FIG. 11B to FIG. 11D illustrates the case where β = 1, β = 2, and β = 3, respectively. Β and γ are determined by the above equations (3a) and (3b).

<Generalized displacement>
In order to treat the lateral buckling as a linear buckling problem, the deformation of each part of the beam 2 due to the lateral buckling is a coordinate value in the material axis direction (that is, an arbitrary point in the material axis direction of the beam 2 from the left end 2a of the beam 2). It is expressed as a continuous function of length y). At this time, the torsion angle θ _y of the cross section generated in the beam 2 due to the lateral buckling should be smoothly continuous in the material axis direction Y as shown in FIGS. 9A to 9C.

In the present invention, an analytical solution of the elastic lateral buckling moment is derived by approximating the series deformation of each part of the beam 2 due to lateral buckling. Since the lateral buckling does not involve the distortion of the cross section of the beam 2, other deformations necessary for deriving the analytical solution, that is, the deflection δ _{z of the} beam 2 shown in FIG. 9C, the rotation angle θ _{x of} the beam 2 shown in FIG. 9A, The rotation angle θ _z of the lower flange 22 shown in FIG. 9B can be expressed by the following equations (3) to (5), respectively. Thus, the deformation (δ _z , θ _x , θ _z ) of each part of the beam 2 due to lateral buckling can be uniquely expressed by θ _y .

Here, d _b is the thickness center distance between the upper flange 21 and lower flange 22, y is the length of up to any point in the timber axis direction of the beam from one end to the timber axis direction of the reference beam . θ ′ _y represents the first derivative of θ _y . a is an auxiliary variable for integration.

<Potential energy>
When lateral buckling occurs in the beam 2, the total potential energy の of this system is given by the following equation (6).

Here, ΔU is the strain energy of the beam 2 and ΔT is the potential energy of the external force.

Next, ΔU is given by the following equation (7) as the sum of strain energy due to bending torsion and strain energy due to pure torsion.

Here, E is a Young's modulus, I is a cross-sectional secondary moment around the weak axis (Z axis) of the lower flange 22, G is a shear elastic modulus, and J is a Saint-Benant torsional constant. θ ′ _z represents the first derivative of θ _z .

Next, ΔT is given by the following equation (8) as a sum of potential energies of M _cr , V _cr , and W _cr .

Here, θ _{x (l)} and δ _{z (l)} represent θ _x and δ _z of the right end 2a of the beam 2, respectively.

<Approximation of lateral buckling deformation>
Arbitrary θ _y allowed for the beam 2 in which both ends 2a, 2a in the material axis direction Y are fixedly supported can be approximated with arbitrary accuracy by a finite series.

In other words, the Fourier series expansion given by the following equation (9) can be applied to most continuous functions, and the series calculation is simple. The buckling deformation is approximated by

On the other hand, in the present invention, when both ends 2a, 2a of the beam 2 are fixed by rigid joining, as the lateral buckling deformation of the beam 2 in which both ends 2a, 2a in the material axis direction Y are fixedly supported, In particular, θ _y can be approximated by a series given by the following equation (10).

Here, a _n is the undetermined coefficients of the n items. When solving the asymmetric buckling, k is set to 2.
When solving the symmetric buckling, k is set to 1 and the above equation (10) is applied to a half of the length l of the beam 2.

<Derivation of elastic lateral buckling moment>
From the principle of minimum potential energy, substituting the above formulas (7) and (8) into the following formula (11) and further substituting the above formulas (1) to (5), the elastic lateral buckling moment The following equation (12) can be obtained as a basic equation.

Here, A, B, C, and D are functional functions of θ _y shown in the following formulas (13) to (16), and l in each formula disappears by integration, so these are determined only by θ _y. It becomes a coefficient.

Here, β and γ are coefficients determined from the above equations (1) and (2) according to the presupposed load conditions V _cr and W _cr . L is the length of the beam 2 in the material axis direction Y, E is the Young's modulus, I is the secondary moment of inertia about the weak axis of the lower flange 22, G is the shear elastic modulus, J is the sun torsional constant of safe, d _b is the thickness center distance between the upper flange 21 and lower flange 22, y is from one end portion serving as a timber axis direction of the reference beam to any point of the timber axis beam length That's it. θ _y is a torsion angle generated in the beam 2 by lateral buckling. theta _'y is the first derivative of θ _y, θ _"y is .a representing the second derivative of theta _y are auxiliary variables for integration.

By the way, the above equation (12) is a linear sum of the yield strength against bending torsion and the yield strength against pure torsion, and generally B ≠ A. Note that the design method disclosed in Japanese Patent Application Laid-Open No. 2016-23446 differs in the two proof stresses when an antisymmetric bending moment acts on the beam 2 in which the lateral movement of the upper flange 21 is restricted. A correction factor is given to propose a high-accuracy approximate solution of elastic lateral buckling moment.

<Minimum conditions>
An analytical solution of the elastic lateral buckling moment is obtained for the case where θ _y is approximated by the series of the above equation (9) or (10). Undetermined coefficient sequence (a _n) requirements to minimize equation (12) with respect to is determined from the following equation (17), we obtained the following equation (18) by performing these differential. In addition, f _nm in the following formula (18) is represented by the following formula (19).

Here, L _nm , M _nm , N _nm , and O _nm in the above equation (19) are expressed by the following equations (20) to (23).

Here, θ _n represents the nth basis function of the series approximating θ _y . For example, the following equation (24) is obtained with respect to the above equation (10). Here, θ ′ _n and θ ″ _n represent the first and second derivatives of θ _n , respectively.

<Analysis solution>
The (17) equation is undetermined coefficients _{a 1, a 2, ...,} when providing a value other than zero for at least one _{a n,} the possibility of buckling occurs. For this reason, the determinant of the coefficient matrix of the above equation (17) must be zero. That is, an analytical solution of the elastic lateral buckling moment can be obtained by solving the Nth order equation of the following equation (25).

Further, the analytical solution of the elastic lateral buckling moment when θ _y is approximated by the third term partial sum of the series of the above formula (9) or (10) is given by the following formulas (26) to (33). .

At this time, the minimum positive value in the actual solution of the equation (26) is the primary elastic lateral buckling moment of the beam 2. The H-section steel 1 is used as a beam 2 extending in the material axis direction Y, and both end portions 2a and 2a in the material axis direction Y are fixed, and in the intermediate portion 2b in the material axis direction Y, the width direction of the beam 2 Under the conditions in which the lateral movement of X is constrained, an intermediate load acts on the upper flange 21 from above, and end loads act on both ends 2a, 2a of the beam 2 in the material axis direction, (16) based on the elastic Lateral buckling moment M _cr of the beam 2, which is calculated from the formula, such does not occur Lateral buckling the beam 2, the upper limit of the surface treatment economics Ix / Lp is determined is preferred.
In other words, assuming that the proof stress coefficient is 1.0 as in the conventional design method described above, more specifically, the design proof strength Mcn calculated by the design method of the present invention is not significantly smaller than the total plastic moment Mp. The square root of the value obtained by dividing the total plastic moment Mp by the elastic lateral buckling moment M _cr calculated from the following equations (12) to (16) is 0.6 or less (√ (Mp / M _cr ) ≦ 0.6). Thus, the upper limit value of the surface treatment economics Ix / Lp is determined, and each dimension of the H-section steel 1 (height dimension H, width dimension W, web plate thickness tw, and flange is set to be equal to or less than the upper limit value. It is preferable to set the plate thickness tf). As an example of this case, the upper limit value of the surface treatment economics Ix / Lp is determined so that Mcn / Mp ≧ 0.95 is satisfied for Mcn when the buckling stiffening interval Lb is about 15 times H. To do.

Here, β and γ are coefficients determined from the following equations (1) and (2) according to the presupposed load conditions V _cr and W _cr . V _cr is a shearing force acting on the end 2 a of the beam 2 in the material axial direction Y, and W _cr is an intermediate load acting on the intermediate portion 2 b of the beam 2 in the material axial direction Y.
1 is the length of the beam 2 in the material axis direction Y, E is the Young's modulus, I is the secondary moment of inertia about the weak axis of the lower flange 22, G is the shear elastic modulus, J is the sun torsional constant of safe, d _b is the thickness center distance between the upper flange 21 and lower flange 22, y is from one end portion serving as a timber axis direction of the reference beam to any point of the timber axis beam length That's it. θ _y is a torsion angle generated in the beam 2 by lateral buckling. theta _'y is the first derivative of θ _y, θ _"y is .a representing the second derivative of theta _y are auxiliary variables for integration.

Note that the above-described design method is preferably realized by a computer device (not shown) that executes a program recorded on a tangible recording medium (not shown) that is not temporary by a CPU (not shown). In this case, the computer device executes the design method described above in response to a command from the input device operated by the operator, and each dimension of the H-section steel 1 (height dimension H, width dimension W, web plate thickness). It is preferable to output tw and the flange plate thickness tf) as design results. The output design result is preferably output so as to be visible via an output device (not shown).

In accordance with the design results (each dimension: height dimension H, width dimension W, web plate thickness tw, and flange plate thickness tf) set by executing the design method described above, the H-section steel 1 is obtained by an existing rolling technique. It is preferable to manufacture. Thereby, the H-section steel 1 of each dimension (height dimension H, width dimension W, web board thickness tw, and flange board thickness tf) prescribed | regulated by the design method mentioned above can be obtained.

As shown in FIG. 10, under the conventional design method, if the height dimension H of the beam 2 is simply increased, the bending rigidity can be improved, but the bending strength of the beam 2 is lowered and the lateral buckling strength is lowered. Therefore, the improvement which made the bending rigidity and the lateral buckling strength of the beam 2 compatible was not able to be performed.

In contrast, H-shaped steel 1 according to the present embodiment, under the design method of the present invention, the above (12) to (16) the elastic Lateral Buckling moment M _cr of the beam 2, which is calculated from the equation Based on this, the upper limit value of the surface treatment economics Ix / Lp is determined. Therefore, in the H-section steel 1, the cross-sectional area S of the beam 2 is reduced, and the surface treatment economy Ix / Lp is improved, and at the same time, not only the bending rigidity of the beam 2 but also the bending strength can be kept high. Therefore, it is possible to improve both the bending rigidity and the lateral buckling strength of the beam 2.

Table 2 shows Examples 1 to 5 and shows a comparison with the conventional design method in the design strength of the bending material to be the beam 2. The calculation of the design strength of the bending material performed here is as follows. For the conventional design method, the yield strength coefficient is set to 1. based on the calculation of the H-shaped cross section shown in the steel structure limit state design guideline and explanation of the Architectural Institute of Japan. Calculate as 0. In the calculation of the embodiment based on the design method of the present invention, the derivation formula of the elastic lateral buckling moment shown in the same book is replaced with the above equation (12), and the proof stress coefficient is 1.0 as in the conventional design method. did.
In the example shown here, in order to compare the conventional design method with the design method of the present invention, the proof stress coefficient is set to 1.0, but the proof stress coefficient can be appropriately set according to the actual situation. In the design method of the present invention, the derivation formula of the elastic lateral buckling moment is given by the above formula (12). However, in the actual member design, the elasticity of the steel material is considered after taking into account the influence of the yield of the steel material and initial imperfections. It is necessary to convert the lateral buckling moment into the design strength. Here, as described above, an example based on the Japan Institute of Architectural Steel Structural Limit State Design Guidelines and explanations is shown, but the conversion calculation from the elastic lateral buckling moment shown in this document to the design strength is in accordance with other design guidelines and design standards. Also good. The bending moment acting on the H-shaped steel beam is calculated for the case where a vertical load is applied (broken line) to the beam subjected to the reverse bending due to the horizontal load shown in FIG. 13 (broken line). Similar effects can be obtained in other load cases shown in FIG. 11D.

Example 1 (H1150 × W300 × tw32 × tf40) to which the present invention is applied, Example 2 (H1100 × W280 × tw16 × tf30), Example 3 (H1000 × W250 × tw12 × tf16), Example 4 (H950 × The effects of the present invention will be described with reference to Table 2 for each of W250 × tw11 × tf25) and Example 5 (H850 × W200 × tw10 × tf16).

Table 2 shows the secondary moment of inertia around the strong axis (Ix), the plastic section modulus around the strong axis (Zxp), the design strength of the steel (F), and the total plastic moment expressed by the product of Zxp and F. (Mp) is shown in columns A to D, respectively. Note that F in Table 2 is a design reference strength (a value called a steel material F value) determined based on the yield point of the steel material. In addition, you may use the yield strength of steel materials as F. In the embodiment, although the F and ^{325N / mm 2 ~ 385N / mm} 2, the present invention has to provide a resilient buckling moment, the value of the F value can be used widely.
In Table 2, columns E to G are calculated based on the design method of the present invention (calculation results based on the present invention), and columns H to J are calculated based on the conventional design method (conventional technology). Comparison results between the design method of the present invention and the conventional design method are shown in the K and L columns. The row E is the buckling length (Lon) that can be obtained without the lateral buckling stiffening calculated based on the design method of the present invention, and the row H is the buckling that can be done without the lateral buckling stiffening calculated based on the conventional design method. The length (Loc) is compared in the K column.
It can be seen from the numerical values shown in the K column that the length capable of eliminating buckling stiffening can be increased by four times or more based on the design method of the present invention. In addition, from the numerical values shown in the K column, when the rolled H-section steel with high surface treatment economy shown in the examples in the conventional design method is manufactured, the structural economy cannot be maintained, that is, many lateral buckling compensations. Since it is necessary to install a rigid material, it is shown that such a rolled H-section steel with high surface treatment economy has not been used conventionally.
The value (Lon) indicated by the E column is the limit buckling length (Lon) that can exhibit the total plastic moment (Mp) without installing lateral buckling stiffening in the design method of the present invention. Therefore, the ratio of Mcn to the total plastic moment Mp is 1.0 as shown in the G column. When the same numerical value is 1.0, the steel material F value is not reduced, and the steel material F value can be used as it is as a short-term allowable stress degree for lateral buckling. On the other hand, the design strength Mcc shown in row I was set to the same limit buckling length (Lon) as the design method of the present invention based on the conventional design method, and the design strength in the case where no lateral stiffener was provided was calculated. Is. The ratio of the design proof stress Mcc to the total plastic moment Mp is 0.52 at the maximum as shown in the J column, and the minimum decreases to 0.28. From this low value, it can be understood that the conventional design method does not produce the rolled H-section steel with high surface treatment economy shown in the examples.
The values shown in the L column indicate a comparison of design strength in Lon. It can be seen that the design strength based on the design method of the present invention ranges from 1.9 times to 3.8 times that of the conventional design method.

Here, the buckling length Lon is a buckling length calculated so that the design proof stress Mcn based on the present invention is the same value as the total plastic moment Mp. The buckling length Loc is a buckling length calculated so that the design proof stress Mcc based on the conventional design method becomes the same value as the total plastic moment Mp.

In Table 2, the present invention was compared with the prior art with respect to the design method after making the examples constant. In Table 3, the significance of the present invention will be described through determining the rolled H-section steel in the range defined as the prior art in FIG. 6 for each of the Examples and making a specific comparison with them.
For each of the examples already shown, the height dimension H and the width dimension W of the H-section steel so that the web thickness tw and the flange thickness tf are constant and the prior art, that is, k is less than 6.1. It was set. That is, H1050 × W404 × tw32 × tw40 as Comparative Example 1 for Example 1, H1000 × W369 × tw16 × tf30 as Comparative Example 2 for Example 2, and H900 × W352 × tw12 × as Comparative Example 3 for Example 3. As tf16, H900 × W291 × tw11 × tf25 is set as Comparative Example 4 with respect to Example 4, and H800 × W243 × tw10 × tf16 is set as Comparative Example 5 with respect to Example 5.
Columns A to C in Table 3 show the secondary moment of inertia (Ix), the plastic section modulus (Zxp), and the steel material F value (F) around the strong axis in this order. The total plastic moment (Mp) calculated as the product of Zxp and F is shown in the D column, the cross-sectional area (S) is shown in the E column, and the outer peripheral length (Lp) is shown in the F column.
In order to compare the example and the comparative example, the design strength of lateral buckling is required. Here, based on the design strength (M15) when the buckling length Lb is 15 times the height dimension H. Is going. The design yield strength (M15) of the rolled H-section steel is the same as the conditions shown in Table 2, and the respective calculation results are as shown in the H column. The G column shows the ratio of the design strength (M15) to the total plastic strength (Mp). As shown in the G column, it can be seen that F does not decrease in the example, but F decreases in the ratio of 0.45 to 0.76 in the comparative example.

The superiority of the embodiment over the comparative example can be confirmed by the values from the I column to the N column. Each column shows a relative value of each value of the example when each value of the comparative example is 1. The Ix values in the examples are all 1.00 because the dimensions are determined so that Ix in the comparative example matches the examples. From the values in the J column, it can be seen that the relative value of the example in Zxp of the example decreases in the range of 0.93 to 0.96. This is because the height dimension (H) of the example is larger than that of the comparative example.
From the values in the K and L rows, it can be seen that the cross-sectional area (S) decreases in the range of 0.90 to 0.94, and the outer peripheral length (Lp) decreases in the range of 0.93 to 0.98. .
Further, it can be seen from the values in the M row that the design yield strength (M15) increases in the range of 1.05 to 2.29. The performance needs to be comprehensively evaluated. For example, among the values shown in the I column to the M column, Ix and Zxp, which are the larger values, are the numerator, and S, which is the smaller value, is the desirable value. Reference values derived from Lp in the denominator are shown in the N column.
Based on this index, it can be said that the performance is improved in the magnification range of 1.21 to 2.50 over the prior art.

Thus, in the H-section steel 1 according to the present embodiment, the cross-sectional area S of the beam 2 is reduced, the surface treatment economy Ix / Lp is improved, and at the same time, not only the bending rigidity of the beam 2 but also the bending strength is kept high. be able to. That is, the H-section steel 1 according to the present embodiment improves the bending rigidity and lateral buckling strength of the beam 2 while improving the bending rigidity and lateral buckling strength of the beam 2 while suppressing local fracture phenomenon due to local buckling of the beam 2. Costs for surface treatment such as painting can be reduced.

In the H-section steel 1 according to the present embodiment, the lateral buckling deformation of the beam 2 in which the lateral movement is restricted is complicated, but the lateral movement of the beam 2 is restricted, and an intermediate load is applied to the upper flange 21 from above. Under such conditions, the elastic lateral buckling moment M _cr of the beam 2 is calculated from the above equations (12) to (16), so that the elastic lateral buckling moment of such a steel beam can be evaluated with high accuracy. Is possible.

In the H-section steel 1 according to the present embodiment, β is zero when the intermediate load is equal in the material axial direction Y of the beam 2 (symmetric buckling), and the intermediate load is equal in the material axial direction Y of the beam 2. In the case of non-bending (asymmetric buckling), by setting β to a real number in the range of more than 0 and 3 or less, in the case of an equal bending moment where the intermediate load becomes equal bending, In any case, the above equations (12) to (16) are used to evaluate the elastic lateral buckling moment of the steel beam while considering various load conditions assumed for the actual steel beam. It becomes possible to do.

The H-section steel 1 according to this embodiment is preferably approximated by the series of the above equation (10), particularly when θ _y is approximated. The H-section steel 1 according to the present embodiment has a dimensionless lateral buckling strength (= M _cr / Mp) obtained by dividing the elastic lateral buckling moment by the total plastic bending moment when θy is approximated by the third term partial sum. 12A and 12B show an example of an analytical solution of the elastic lateral buckling moment, where the vertical axis represents the slenderness ratio λb obtained by dividing the length 1 of the beam 2 by the beam formation.

At this time, as shown in FIG. 12A, the H-section steel 1 according to the present embodiment has substantially the same analytical solution of the elastic lateral buckling moment when the series of the above equation (10) is used. The bending moment can be evaluated with high accuracy. On the other hand, as shown in FIG. 12B, when the Fourier series of the above equation (9) is used, the analytical solution of the elastic lateral buckling moment varies greatly. At this time, in order to evaluate the elastic lateral buckling moment with high accuracy using the Fourier series of the above equation (9), for example, it is necessary to approximate θ _y by the 10th term partial sum. The analysis calculation becomes complicated.

Thus, the H-section steel 1 to which the present invention is applied approximates θ _y by the series of the above equation (10), thereby avoiding unnecessarily complicated analysis calculation of the elastic lateral buckling moment. The elastic lateral buckling moment of the steel beam can be evaluated with high accuracy.

Tables 4 to 16 show various rolled H-section steels. In Tables 4 to 16, “Example” is a rolled H-section steel (example of the present invention) that satisfies the above formulas (35) to (38), and “Prior art” is a conventional rolled H-shape that does not satisfy these formulas. It is steel. FIG. 14 shows a graph in which the horizontal axis is H / S and the vertical axis is Ix / Lp for each example and each conventional technique in Tables 4 to 16. In FIG. 14, “◯” represents the plot of the example, and “x” represents the plot of the prior art.

Although one embodiment of the present invention has been described above, the above embodiment is presented as an example, and the scope of the present invention is not limited only to the above embodiment. The above embodiments can be implemented in various other forms, and various omissions, replacements, and changes can be made without departing from the spirit of the invention. The above-described embodiments and modifications thereof are included in the invention described in the claims and equivalents thereof, as long as they are included in the scope and gist of the invention.

1: Rolled H-section steel 2: Beam 2a: End 2b: Intermediate part 20: Outer peripheral surface 21: Upper flange 21a: Upper and lower both surfaces 21b: Left and right both end surfaces 22: Lower flange 22a: Upper and lower both surfaces 22b: Left and right both end surfaces 23: Web 23a: Left and right side surfaces 23b: Curve connecting portion (fillet)
25: Shear connector 3: Column 30: Diaphragm 4: Floor slab X: Width direction Y: Material axis direction Z: Height direction

Claims (5)

1. A method of designing a rolled H-section steel having an upper flange and a lower flange, and a web connecting the upper flange and the lower flange, and the outer peripheral surface of the upper flange, the lower flange, and the web being surface-treated. Because
   The value obtained by dividing the cross-sectional secondary moment Ix around the strong axis by the outer peripheral length Lp in the cross-sectional shape when viewed in a cross-section perpendicular to the material axis direction is the surface treatment economic Ix / Lp, and the area of the cross-sectional shape is S When satisfying the following expressions (35) to (38), the height dimension H from the upper flange to the lower flange is 700 mm or more, and the width dimension W of each of the upper flange and the lower flange Is 1/5 or more and 1/2 or less of the height dimension H, the thickness tw of the web is 9 mm or more and 32 mm or less, and the thickness tf of each of the upper flange and the lower flange is 12 mm or more and 40 mm. The method for designing rolled H-section steel, wherein the height dimension H, the width dimension W, the plate thickness tw, and the plate thickness tf are set as follows.
   

   
2. The rolled H-shaped steel is used as a beam extending in the material axis direction and both ends of the rolled H-shaped steel in the material axis direction are fixed. Under the condition that the lateral movement of the steel in the width direction is constrained, and under the condition that an intermediate load acts on the upper flange from above and end loads act on both ends in the material axis direction, the following equation (12) Using the elastic lateral buckling moment M _cr of the beam calculated from the equations (16), the height dimension H, the width dimension W, the plate thickness tw, and the thickness so as not to cause lateral buckling of the beam. The method for designing a rolled H-section steel according to claim 1, wherein a thickness tf is set.
   However, V _cr : Shear force acting on the end of the beam in the material axis direction, W _cr : Intermediate load acting on the intermediate portion of the beam in the material axis direction, β and γ: Loads V _cr and W _cr ) And coefficients determined from the formula (2), l: length of the beam in the axial direction, E: Young's modulus, I: secondary moment of inertia around the weak axis of the lower flange, G: shear modulus, J: sun · torsional constant of safe, d _b: plate thickness center distance between the upper and lower flanges, y: from one end thereof in a timber axis direction of the reference beam to any point of the timber axis direction of the beam length, theta _y: Lateral torsion angle caused in the beam by bending, θ _'y: the first derivative of θ _y, θ _"y: second differential of θ _y, a: a parametric for integration.
   

   

   
3. Wherein as the square root of the value of the full plastic moment Mp divided by the elastic Lateral Buckling moment M _cr rolled H-shaped steel is 0.6 or less, the height H, the width W, the thickness tw, The method for designing a rolled H-section steel according to claim 2, wherein the thickness tf is set.
4. An upper flange and a lower flange;
   A web connecting these upper and lower flanges;
   A rolled H-section steel comprising
   The upper flange, the lower flange, and the outer peripheral surface of the web are surface treated;
   A height dimension H from the upper flange to the lower flange is 700 mm or more;
   The width dimension W of each of the upper flange and the lower flange is not less than 1/5 and not more than 1/2 of the height dimension H;
   The thickness tw of the web is 9 mm or more and 32 mm or less;
   A plate thickness tf of each of the upper flange and the lower flange is 12 mm or more and 40 mm or less;
   The value obtained by dividing the cross-sectional secondary moment Ix around the strong axis by the outer peripheral length Lp in the cross-sectional shape when viewed in a cross-section perpendicular to the material axis direction is the surface treatment economic Ix / Lp, and the area of the cross-sectional shape is S Then, the height dimension H, the width dimension W, the plate thickness tw, and the plate thickness tf satisfy the following formulas (35) to (38);
   A rolled H-section steel characterized by that.
   

   
5. The rolled H-shape having the height dimension H, the width dimension W, the sheet thickness tw, and the sheet thickness tf set by the method for designing rolled H-section steel according to any one of claims 1 to 3. A method for producing rolled H-section steel, which produces steel.

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