SU49258A1 - An instrument for drawing lines affecting uncut beams and the like. - Google Patents

Description

Influence lines or influent lines are used in the calculation of engineering structures subjected to the action of a moving load: continuous bridge trusses and beams, crane girders of industrial and port facilities, continuous beams of bridges, conveyors, etc.

There are the following ways to build influential lines: 1) analytical, 2) graphic, 3) graphic-analytical (mixed), 4) building lines of influence using tables compiled for particular cases, 5) building lines of influence using instruments (Gottschalka Influentiograph Colonett and others.).

The construction of lines of influence by the first three methods is associated with the volume of graphic and computational work.

The construction of the lines of influence by the fourth method is limited, since the tables in the literature cover practice cases to a small extent. Existing instruments for building lines of influence are more suitable for demonstration purposes than for building lines of influence in the design of a structure.

The proposed device makes it possible to automatically build influent lines for continuous beams with an unlimited number of spans, with any ratio of the moments of inertia and lengths of individual spans, with free support or elastic embedment on the extreme supports.

The construction of influence lines using the proposed device has the following advantages over the methods listed above:

1) frees the energy of the calculator from computational and graphical work and the inevitable errors associated with it;

2) accelerates work several dozen times;

3) allows to attract to the construction of influent lines of persons who do not have special qualifications;

4) the influence lines built using the instrument are continuous and are distinguished by increased accuracy (when using a Vernier on installation mechanisms and with an appropriate choice of scale).

In the proposed tool for drawing the influence lines, a cone mounted on a rotatable axis with a street-shaped cross section is applied, to the surface of which the end of the loaded blue rod is pressed, through a two-arm lever that controls the movement of the writing device drawing the desired line drawing the desired axis drawing the desired device. perpendicular to the direction of movement of the writing device by a paper tape. In FIG. 1 depicts a general view of the proposed device;. 2-16 details of the device; FIG. 17 and 29 illustrate an example of constructing influent lines; FIG. 18-21 and 28 illustrate the cone / device design and the method of its construction; FIG. 22-26 and 30 illustrate the mode of operation of the instrument; FIG. 27-to be calculated beam designation design data. The following expressions follow from the Clapeyron equations for the support moments Mn and Mc + 1 span loaded with a mobile force P 1 (see Akimov-Peretz D. Ya. Statics of Structures 4/1 p. 156). „(4 - ,,) S-f- As 71 II a I, and I .j; .5+.;, - (35o). . (I) / and. , -four(-"") . S.- o I -f-. L, + (350 (see Fig. 27 of the drawing). Using substitutions; A - - .I., - H.C.–. hJ 1, GC - 4 - a. „- bn /„ - i. -.- g-y + „+1 1De / f ,, and / С - left and right focus relations in the given span, fh rmules (I) and (II) transform 1 into formulas of the following form: F„ (Kl, +) , C -1 M ,,,., (K, l} 1, (IV); Denote I by L S (K ,, +}) 33 through a. (V) 5 (/ C, + 1) - 35o through. (We have: Mn-Aa; M ,, 4. In the formulas V and V with C —r - T 1535o. In the polar coordinate system at constant values of A ,, and K "of the equation (V) and (VI) represents a curve-like curve (Fig. 18), with equations (V) and (VI) representing the same curve, If the angle y is taken over the polar angle and the angle is set aside when plotting the curve in opposite directions. In a rectangular coordinate system with a constant value of equation (V) and (VJ) represent a straight line. p can be represented as distances from the longitudinal axis to the outer surface of the body shown in fig. 19. To clarify the following, the construction of the drum cross sections is given. It is known from the theory of continuous beams that the minimum value of K "(or Kp) is 2. For practical purposes, the maximum value of these same values is sufficiently taken to be 20. Table 1 contains the values of a (equation V) for / C 2 and and anacheni p (equation VI) with u ,, 20.

When compiling Table A, it is assumed to vary in 0.1. FIG. 20, the curve is plotted as K = 2. In FIG. 21 built curve at.

In the first and second cases, the values of "1," 2 ... ttg were postponed not from the origin of coordinates, but from the intersection points of the circle with the radii - vectors.

Table 1 shows that a. - c ,, hell p7, a, rb, “sHPs, etc .; thus equations (V) and (VI)

are the equations of the same curve if the polar angle readings are in opposite directions.

When constructing the curve and the readout is made in the course of an hour hand.

Therefore, for curve p, the counting must be performed counterclockwise.

The sections shown in FIG. 20 and 21 are cone bases. The longitudinal axis of the cone passes through points O and O (Fig. 19).

Table 1.

The side surface of the cone / is formed by the movement of the straight line P - P (Fig. 19).

It is easy to make sure that the point of the curves of the intermediate seni of the cone (with the same value of A) lies on the straight line.

For example, with .Y 0,4 and K „II

we have:

  11 and a 0.384 (ll-fi) - 0,, 888

since / s 11 is the midpoint of the interval between / C, 2 and

A: „2)

LH „2

On,

0.432 f 7.3444

 3,888. 2

A section of the cone with the DD plane along the longitudinal axis is shown in FIG. 28

The cone / (fig. 1), with the help of screw 2 and clutch 3, which freely covers the drum neck (fig. 9), is able to move along shaft 4. Shaft 4 and screw 2 have shoulders 5 at the ends and do not move along axes. The screw 2 has at the other end a gear 6 and a head 8 with a grooved rim for rotating the screw with fingers. Gear B is mated to the gear wheel of the installation drum 7 (Fig. 7). On the installation drum 7 a uniform scale of values of / С „and АГ / is applied, from 2 to 20.

The shaft 4, and with it the cone / is driven into rotation by the crank handle 9 by means of a worm gear // and a bevel gear transmission 12. The first transmits rotation from the JO shaft to the shaft of the cone 39 (Fig. 6), and the second transmits rotation from shaft cone 39 shaft 4.

The slider / J with spring M is in constant contact with its tip / 5 with the surface of the cone /.

FIG. 22, the dotted lines show the two extreme positions of the cone 7 — left and right. In the first case, with the rotation of the cone / tip of the slider J3, it will be in contact with the curve shown in FIG. 21, and in the second case, with the curve shown in FIG. 20.

To translate the cone / from the right to the left position, it is necessary to make several turns of the shaft 2.

In this case, the drum 7 will make 1 turn. Having a uniform scale on the drum 7 from 2 to 20, it is possible to set the cone / to a certain intermediate position, according to the value K «(or Kp).

The tool 77 (to be described later) and the slider J3, having the guides J6 and / 8, can be moved in directions parallel to each other. The slider 75 and the device 77 are connected by a lever 20, passing freely through the hinge drums 21. The hinged drums 27 (Fig. 10) enable the lever 20 to move to the positions shown in Figs. 12 dotted line. The middle drum is placed on the extension of the nut 22, with the displacement of which the ratio of the arms of the lever 20 changes.

The nut 22 is moved by a screw 23 having a gear 25 at the end and a head 24 with a ribbed rim. Gear 25 is matched to gear 26.

On the installation drum, a uniform scale of values greater and less than units is applied.

FIG. 2 shows the position of the nut 22 when mounted on a unit drum 26. In this case, the movements of the slider 75 and the tool 77 are equal. When 26 values less than one are set on the drum, the nut will be in the right half and when setting values greater than one, the nut will be in the left half.

To clarify in FIG. 30 shows the position of the nut 22 when mounted on the drum 26 of a value of 0.5 and shows the position of the nut when installing 1.8.

The tool 77 (Fig. 24) consists of two gear racks 27 and 28 moving parallel to each other in the cage 29. The slats 27 and 28, together with the cage 29, can be moved in the guide 30 fixed on the body of the device.

A pinion gear 57, which is fixedly connected to the axis 52, rotates in the recesses of the holder 29 and moves the rail 28 in the direction opposite to the movement of the rack 27 when moving the rail 27.

FIG. 13 and 14 shows a device placed on the yoke 29 against the axis of the gear 52. The device consists of a strip 55 with a wedge-shaped slot. The plank can be transferred by hand to the upper or lower position, which is fixed by a latch.

At the upper position of the bar (Fig. 14), the axis 32 will be clamped with grooved surfaces of the slot of the bar.

Consequently, the rails 27 and 28 together with the guide 29 will move in the direction communicated by the lever 20. When the bar is lowered (Fig. 13), the axis 32, falling into the wide part of the slot of the bar 33, is released and can freely rotate with the gear 5 / in the cage housings 29. The lower end of the bar 33 falls into the recess of the fixed guide 30. This makes the cage 29. The gear rack 27, moving under the action of the lever 20, rotates the released gear. The rotation of the latter drives the rail 28. The movement of the rail 28 takes place in the opposite direction to the movement of the rail 27. The foregoing explanation of FIG. 25 and 26.

FIG. 25 shows the direction of movement of the rails with the top position of the strip, and FIG. 26 shows the direction of movement of the rails with the lower position of the bar 33.

In the first and second cases, the similar position of the laths in the cage is shown in FIG. but. FIG. b shows the position of the slats and the holder after moving the drum 2 / by the value of La (or Lr).

The end of the rail 28 is provided with a recording device 34.

The paper tape 55 (Figs. 1, 2) moves in the directions indicated in Figs. 3 by means of the drive roller 37 and the idler rollers 36. The speed of movement of the paper tape is controlled by a friction gear consisting of cones 38 and 39 (Fig. 6) located on parallel axes, and roller 40 freely rotating in sharpening axis 41.

The gear ratio between the axes of the cones 38 and 39 changes as the roller 40 moves. The roller 40 moves together with the axis 41 by means of an engagement consisting of a rack 42 fixedly connected to the axis 4f and a pinion 43 fixed on the axis 44 ( Fig. 7). The axis rotates in the fixed sleeve 45. At the end of the axis 44, the arrow 46 is fixed to the head 47 with a grooved rim.

The arrow 46 slides in a circle 48 with divisions denoting the size of the spans.

If set with the length scale of the lines drawn by the device

I t 2 cm

It is not difficult to choose gear ratios of gears 72, cones 38 and 39, as well as the diameter of the drive roller so that when mounted on a circle 48 of 2 tons, the paper tape at each full taper rotation / moved 4 cm. When mounted on a scale values of 7.3 tons of paper tape should be moved by 14.6 cm after each complete rotation of the cone /, etc.

The rotation of the axis of the cone 38 is transmitted to the axis of the roller 37 through a gear reversing gear (FIG. 5) consisting of gears 49 and 50 mounted on the bracket 57, teeth of 52 fixed to the axis of the roller 37.

With the left position of the lever 54 (fig. 15), the axes of the cone 38 and the roller 37 will rotate in opposite directions.

With the right position of the lever 54 (FIG. 16), the axes of the cone 38 and the roller 37 will rotate in the same direction.

FIG. The 1 and 2 numbers 55 indicate the bearings of the rotating shafts.

We will assume that the initial position of the cone J is the position at which the tip of the slider 13 is in its recess (9 0).

With this cone position, the tip of the recording device (pencil or pen) coincides with the middle line of the paper tape.

FIG. 1 and 20 are shown by a dotted line.

The slider 13, slipping along the surface of the cone / as it rotates, will move in the guide 16. In connection with this, the lever 2 will assume inclined positions (Fig. 12) and after a complete rotation of the cone 7 will return to its original position. The rail 27, perceived pressure from the lever 20, will also move. As indicated above, the rail 28 may move either in the same direction as the rail 27, or in different directions. When moving

in one direction, the recording device will slide in directions a and b (Fig. 1). When the rails 27 and 28 are moving in different directions, the device J- will slide in the directions c to d.

Both in the first and in the second case, the transition from the direction a to the direction b to c from c to d will occur at the moment when the tip of the slider 75 of the maximum ordinate of the cross-section curve of the cone / passes.

Simultaneously with the rotation of the cone /, the paper tape moves, the direction of movement of which depends on the position of the lever 54.

As a result of the simultaneous movement of the paper tape and the recording device, a curve will be drawn on the tape.

The curve will be convex upward at the lower position of the bar 33 and convex downward at the upper position of the bar 33. If we accept that for the negative support moments of the branch of the influence lines are downward and for positive upwards, then from the above we can derive the following rule: the lines of influence of negative moments, the bar 33 should be in the upper position (Fig. 14), while building the lines of influence of the positive moments, the bar 33 should be in the lower position (Fig. 13).

Let it be necessary to construct the lines of influence of the support moments for the beam shown in FIG. 17

The beam is rigidly fixed on the extreme supports.

Moments of inertia / i / 2.

/ 1, 0.625

L, 0.625

FIG. 29, the lines of influence of the reference points Ж, / Wj and when the load is moved in the first span are drawn, M, MS and Mi are drawn when the load is moved in the second span.

The arrows and the roman numerals around them indicate the direction and sequence of the construction of individual branches of the influence lines.

I. Construction of the line of influence of M when moving the cargo and the first flight is as follows:

/ And,. 4.50.

To build this branch, you need to 1) install 1 - 5 on the 4S disk;

2) on the drum 26 to install / C / 4,5;

3) install Aj 0.625 on the drum 26;

4) bring the bar 33 to the top position; 5) put the lever 54 in a position in which the movement of the paper tape will occur to the left; 6) with a handle 9, make one full turn of the drum on 7 in direction a (Fig. 18).

P. Construction of the line of influence of M. when moving the load in the first span

Ж2 - / 4, “„, - 2.0

1) It is necessary to change the setting Ki on the drum 7 - 4.5 to KI - 2.0 ;; 2) put the lever 54 in a position in which the movement of the paper tape will occur to the right; 3) make a full turn of the cone 7 in the direction l.

Iii. Building a line of influence of M when moving rpysia in the first span

M - 4- -2- 4- 8 20

  / 1 t G 1

A) L 9

1) It is necessary to translate the bar 33 in the lower position; 2) on the drum 26 to change the setting L 0,625 to

0.625

: 0.313;

y,

3) transfer the lever 54 to a position in which the movement of the tape will occur; walk left; 4) make one full turn of the cone / in the direction (Fig. 18).

Table 2 contains indications 1) on the position of the strip 33, 2) the tension of the movement of the paper tape and the cone 7 and 3) about the installations on the drums 7, 26 and the disk 48. These are the guidelines for the construction of six branches of the influence of the reference moments. of the example shown in FIG. 17

Subject and zo.breet eni.

Claims (6)

1. An apparatus for drawing lines of the influence of continuous beams, trusses, etc., characterized by the use of a cone axis mounted on a rotary axis 4 / with a cross section of a street-shaped form, to the surface of which the end of a slider 14 loaded with spring 14 is pressed the movement controller of the writing device 34, drawing on the moving paper perpendicular to the direction of movement of the paper tape, the desired influence lines (Fig. 1). 2. The form of the device according to claim 1, characterized in that, in order to install the slider 13 on the surface of the cone / at a different distance from its base by swapping the cone / along axis 4, the neck of the cone 1 is connected with its free coupling 3, mounted on the screw 2 connected to the installation drum 7 (FIG. 1). 3. The form of the device according to PP. 1 and 2, characterized in that, in order to change the length of the arms of the lever 20, the axis of its rotation is fixed on the process of the nut 22, mounted on the screw 23 connected to the installation drum 26 (Fig. 1). Tabl 4. The form of the device according to PP. 1-S, characterized in that, in order for the device to construct influence lines corresponding to both positive and negative values of the moments acting on the beam, the movements of the end of the lever 20 to the writing device 34 are transmitted to a part of the device made in the form of two prisoners 29 gear racks 27, 28, of which the rail 27 is connected with the lever 20, and the rail 28 is provided with a writing device at the end, which rails are coupled with the gear gear 5 / rigidly mounted on the axis 32, passed through the slot of the bar 33, which serves for locking over stubble 31 and to connect the yoke 29 with the fixed guide 30 with an un-spontaneous gear (Figs. 1, 2, 4). 5. In the device on PP. 1-4, the application of a friction transmission roller 56 which serves to rotate a paper tape 55 roll, consisting of two cones 38, 39 connected by means of a friction roller moving along its axis 41 (Figs. 1, 6). 6. In the device on PP. 1-5, in order to communicate the rotation of the roller 57 in one direction or another, a reversing gear consisting of the gears 49, 50, the gear 52 and the gear 53 (Fig. 5). All the operations to build the line of influence of this example using the instrument will take approximately 3-5 minutes. its 2. .fig.P /  br, mp frntovl, cnt,  l Inin n-l FIG.2V /, 6 I / fig / 3 0/7 l | .r 8a