US2382138A - Composite beam structure - Google Patents

Description

All'. 14, 1945. Q P. CUENI A COMPOSITE BEAM STRUCTURE Filed July 2. 1941 fs f5 2271' l f5 2727 35000 35000 Sg @WHL v1*0/ viil y!!! 50000 2` fsw 30000 57rd .5755! 9505000 .i767 25u00 A n 00A/025m E200@ l en mw fa;-

[0000 (/aooo r5/5 au o Patented Aug. 14, 1945 2,382,138 COMITOSIT BEAM STRUCTURE Clemens Paul Cneni, Arlington, N. J., assignor to Porete Manufacturing Company, North Arlington, N. J., a corporation of New Jersey l Application July 2, 1941, Serial No. 400,851

(Cl. 'l2-71) 9 Claims.

This invention is directed to composite structures wherein combined steel and concrete members are designed to carry predetermined loads.

Structures of this type have been known and used for a long time, including such composite structures in which a series of steel beams, suitably supported by pillars or other permanent members, carry a reinforced concrete slab in which metallic members, such as cleats, prongs, rods, and elements of various shapes, are attached to or in contact with such steel beams so that the concrete slab is securely anchored to the steel beams to form the desired composite structure. In all of the composite structures without temporary supports. heretofore used, the steelbeams were always designed to carry the entire dead load, which usuallyconsists of the weight of the steel beams plus the weight of the concrete slab united therewith.

The additional strength present in the composite structure becomes available for the carrying of live loads only after the concrete slab has set. The steel beams were designed to carry their own weight and that of the concrete slab during the pouring and setting period, unless temporary intermediate supports were provided. However, such temporary supports added considerably to the expense of the construction, in that it required considerable labor for the erection, mate'- rials to be used therein, and ya considerable amount of labor for the removal of such temporary supports. Continuous supports for the full length of the beams are impractical and in most cases far too expensive. Therefore, the

temporary supports are usually spaced far apart and initial tensile stresses occur in the bottom of the steel sections between the supports. Fur-v thermore, such supports were not completely leffective, so that the initial stresses in the steel beams were almost as high where supports were used as where such supports were omitted.

The steel beams in have the gre test fiber stress in the extreme portion of the and bottom. This extreme fiber stress vis normally much below the allowable stress, which is usually 18,000 lbs. per square inch.

The difference, 18,000 minus the extreme fiberv available te the composite section to stresses, is carry the additional dead load and the live load. For instance, if the steel section is stressed by its section, therefore, did not exceed the allowable carrying this dead load will i own weight. and the dead load of the concrete slab l to say 5000 lbs. per square inch, there will be available for the composite section 18,000 minus 5000l equals 13,000 lbs. per square inch. -This 13,000 lbs. can take care of the tensile stress prostress in the steel. The allowable stresses were usually arrived at by dividing the ultimate strength by an ample factor of safety. For instance, for concrete theultimate strength at 28 days was divided byl2.5 to 4, and for structural steel the yield point was divided by about 2. It was generally regarded as essential to sound engineering that the initial stresses in the steel due to the dead load should be taken into considera.- tion in designing any composite section.

It is among the objects of the present invention to provide a new and useful design of composite structures involving the use of steel beam. and concrete members united therewith in which the design for a speciiic load is derived by the use oi factors not heretofore lmown in the art.

It is among the objects of the present invention to provide a structure -of steel and concrete wherein for a predetermined load, the steel area or the weight of the required steel is reduced substantially without impairing the carryin! capacity of the composite section and with .a reduction in the weight of the complete structure.

It `has now been determined by theoretical investigation and by tests that a well designed composite section may be so computed as to reduce the area and, therefore, the weight of the steel section by a substantial amount 'without reducing the normalfactor of safety. Actually the factor of safety is still higher than for conventional designs.

The present invention is based upon the discovery that in two similar composite sections. one without and the other with temporary intermediate supports during pouring and setting of the concrete, at the moment -of failure, ultimate stresses are reached simultaneously in steel and concrete, and about at the same load, in both sections, despite the initial stresses due to the dead load in the section without temporary supports.

This behavior may partly be explained by the fact that the stress-strain diagram of the steel is not exactly the same as that of the concrete. Itis no longer a straight line from the mom'ent the steel is stressed to the elastic limit. The deviation from the straight line increases until. at

the moment the yield point in the steel is reached.v deformations increase without an increase in stress. The stress-strain diagram of the concrete also shows a deviation from the straight line, from the moment the yield point is reached in the concrete. but by far not as pronounced as it is for steel, and there is never an increase in deformation without an increase in stress.

The stresses in the steel due to the dead load remain there, but the concrete takes more stresses from the live load and between the reaching of the elastic limit in the steel and the ultimate failure, the concrete, proportionately. takes so much more of the live load stresses that at the moment of failure the stresses are distributed in steel and concrete as if tbe concrete had participated in carrying the dead load. In other words. shortly before failure the stress distribution is the same as in a composite section. where the steel beam is temporarily supported during pouring and settlngof the concrete, and in which steel and concrete participate in carrying the dead load as soon as the temporary supports are removed. Therefore, in the design of any composite section which has an effective shear reinforcement, it is safe to assume that the composite section carries both' the dead and live load. and to disregard all initial stresses in the steel which may be produced by the dead load due to no temporary supports or due to supports which are not eii'ective.v However, enough concrete area must be provided so that the concrete is able to take care of additional stresses for an amount equal to that required bythe dead load if it were acting on the `composite section.

In previous designs, certain well established formulas have been used. For instance. in com puting the tensile stress in the steel, the following formula had been used:

In said formula. the reference character l. represents the unit tensile stress in the extreme ber of the steel. MM represents the moment due to the dead load. MLM represents the moment due to the live load. S'. represents the section modulus of the steel section alone, and 8 represents the section modulus of the steel section of the composite section. .The term "dead load as used herein includes the weight of the beam plus the nrst pour of concrete. The term "live load as used herein includes the second pour of concrete. such as for example in a bridge. a wearing surface, concrete railings, additional road bed, and the like. 'I'he live load also includes the additional dead load such as paving blocks. pipes. ilooriill. and the like. In addition. the term includes the normal live load. namely. the temporary loading of the structure due to trame and the like.

According to the prior art, the formula used for computing the compressive stress of the concrete of a composite section without temporary supports was as follows: v

Miha fe ngt--- (No. 2)

In this formula le represents the unit compres-` sive stress in the extreme iiber of the concrete. and Be represents the section modulus of the concrete in compression of the composite section. These formulas were us'ed in prior designs for computing the elements of the composite' sections where no temporary supports were usedin the construction of the structure in question.

According to the present invention. -a diderent system of computation is used which is based upon the theory that the composite section car- .ries the total load and thereare disregarded any initial stresses in the steel dueto tliedead load where ineffective or no temporary supports are used. In computing the tensile stress in the steel. the following formula is used in accordance with the present invention:

. f. M i.lg4: M 1 (No. a)

Se (No. 4)

Comparing this formula with the previously used Formula No. 2, it will be seen that in computing the stress in the concrete. consideration has been given to the dead load which had previously been ignored in prior formulas for computing thc stresses in the concrete.

In the accompanying drawing. constituting a part hereof, and in which like referencecharacters indicate like parts, f

Fig. l, c and b, are stress-strain diagram o steel and concrete, c the diagram of deforma tion of a composite section: l

Fig. 2. a, is a cross-sectional view of a composite beam, b; c, d and e are `stress ldiagrams of that beam for different loads;

Fig. 3 is a cross-sectional view of a composite beam with no concrete cast about the steel section;

Fig. 4 is a cross-sectional view of a composite beam in which the steel section is entirely embedded in the concrete Fig. 5 is a cross-sectional view of a composite beaml with no concrete cast about the steel section; and f Pig. 6 isa longitudinal view showing a composite beam suitably supported on permanent supports subjected to a live load. v

In Fig. 1a is shown the stress-strain or stressthat for steel, n being the ratio of the modulus of elasticity of steeitothat of concrete (E. A. E

'El is generally assumed to be 30,000,000 lbs. per

square inch. For this'particular demonstration the Es is assumed to be 4,545,000 lbs. per square inch, which determines n=8.6 and which corresponds to an average concrete `for oors in bridges or high class buildings with an ultimate strength of about 4500 lbs. per square inch. On

thesimilarityofthesetwciu'vesarebasedthe design formulas generally used for reinforced or practically so, the stresses in steel and conconcrete and also for composite sections of steel and concrete. If the two curves were not similar. the assumption that increments of a load applied consecutively to a reinforced concrete beam increase the stress in the steel and in the concrete in a certain ratio and for each increment for the same amount would be false. However, there is one difference between the two curves. As pointed out before, both curves deviate from a straight line from the moment the yield point is reached in the respective material. The deviation of the concrete curve is gradual, the curve has no abrupt changes. The deviation of the steel curve, starting after-the stresses reach the elastic limit. increases rapidly until the yield point is reached. Then an abrupt change takes place. To effect an increase in defamation, an increase in stress was required until the yield point was reached, but now deformation increases without an increase in stress or even with a reduction in stress, as is shown by the downward direction of the steel curve at `this point. This dissimilarity in the two curves is of smalllmportance in usual reinforced concrete or composite designs, but it may be of considerable importance in composite sections with pre-stresses in the steel, as will be explained later.

In Fig. 1b, the same two curves I andv 2 are shown but in a different position to each other. It must be remembered that in a composite section, without temporary supports when the concrete starts to take compresive stresses. the steel already has stresses due to the pre-stresses produced by the dead load. The two curves, therefore, do not start on the same level. Por the present demonstration `it is assumed that the dead load produces pre-stresses of 0000 lbs. per square inch. 'I'he concrete curve then starts at the level 9000 of the steel curve. 'Ihe actual conditions, however, are not yet correctly represented. It is common practice to use a much higher factor of safety for the concrete than for the steel. 2 to 2.5 is normal for steeibut 2.5 is the minimum for concrete and 8 to 4 may be an average for bridge decks and 2.5 to 3.5 an average for floor. in buildings. Assuming the yield point of the steel is 39,000 lbs. perl square inch, and the allowable stress 18,000 lbs. per square inch, then the factor of safety for the steel is 2.2. Assuming the ultimate strength of the concrete is 4000 lbs. per square inch and the allowable stress 1000 lbs. per square inch the factor of safety for concrete is 4. Por steel the determining factor for ultimate strength in a composite structure is theI yield point, for concrete it is the intimate compressive strength. This difference is due to the above-mentioned difference in the two stress-strain curves. If a load is applied, producing a. stress in the steel of 4500 lbs. per square inch, it is 25% of the allowable steel stress and 11.30% of the ultimate strength (yield point). According to the reinforced concrete theory the same load increases the stress in the concrete by 25% of the allowable stress that is by 250 lbs. per square inch. Y The increase in per cent of the' ultimate stress of concrete, however, is only 6.25%, or less (11.3$-0.25=5.11). In other words, the deformation in the steel produced by a certain load has to be compared with the deformationproduced in the concrete by aload about 45% lower. Inthiswaycurvelisdeterminedasshownin Flg.lb.

Aslongasthecurvesland l areidentical crete will remain at the same ratio. If a load produces comparatively more deformation in the steel than in the concrete, then the concrete will takel more stresses than assumed in the design.

A comparison of curve l with curve l shows that this actually happens and at an increasing rate as the load increases. Once the stresses in the steel approach the yield point, the discrepancy between the two curves is considerable, and the concrete will take considerablyhigher stresses as assumed in'the design.

A further explanation of this is given in Hg. 1c. In conventional reinforced concrete or :zomposite design, it is assumed that for a certain increment of load there is always a corresponding increase in elongation in the steel and a corresponding increase in contraction in the concrete. The line 4-4' represents the zero line, showing a state of no load and therefore no deformation. A mst increment of a load which will produce deformations is represented by the line 5-5' intersecting the line 4 4' at point 5 indicating the neutral axis of the composite section. If another increment of load is applied producing comparatively a greater deformation in the steel than in the concrete as shown by the line 5 5', the neutral axis moves up to point 6. A moving up of the neutral axis means a comparatively higher stress in the concrete and a comparatively lower stress in the steel. If an elongation in the steel occurs without an increase in stress, as shown by the line 7 1', the neutral axis as shown by intersection point '7 still moves up. As the concrete cannot contract without an additional force, that means that it takes additional stresses even though the stresses in the steel do not increase. Exactly that .happens when the stresses in the steel reach the yield point.

Fig. 2a is a cross section of a composite beam with concrete cast about the steel section. The steel section l may be a rolled I beam or wide flange section, or a built up riveted or welded section, the top flange may be identical to the bottom flange or smaller, and a cover plate may be attached to the bottom flange to increase the steel area. Steel section t is permanently supported at the ends but has no intermediate temporary supports. Attached to the upper part of the steel osection may be a shear reinforcement l in form of a spiral or other to insure an effective bond between steel and concrete. A concrete haunch I0 is cast about the steel section, to protect the steel or increase the bond, supported entirely by the steel section, as is also concrete slab il poured monolithically with the concrete haunch I0. 'I'he concrete slab Il may have cross reinforcement bars in top and bottom i! and longitudinal reinforcing bars Il top and bottom.A

Fig. 2b shows the stress'diagram of the steel section under the dead load, the arrows I4 representing the tensile stresses in the bottom and i5 the compressive stresses in top of the beam. Il being the center of gravity of the steel section.

Fig. 2c `shows the stress diagram of the composite section under live load. At a ilrst increment of load the stress distribution may be rectilinear, as indicated by the line I'l-II the intersection with the zero line being at point Il, through which the neutral axis 2l of the composite section passes. A further incrementof load will produce stresses indicated by the line 2I-22. which is no longer a straight line. The

neutral axis may move up from Il to Fig. 2d shows the combination o( the shear diagram Figs. 2b and 2c, the horizontal arrows 2l represent the tensile stresses in the steel at the bottom of the'steel section. The arrows Il' at the top oi the steel section show the remain-` ing compressive stresses in the steel due to the dead load. The horizontal arrows 2l represent the compressive stresses in the concrete. The stress distribution is no longer rectilinear as seen by comparing it with the dotted line lI-II.

Fig. 2e shows the stress diagram of the com posite section at the moment failure starts. in other words,at the moment the stresses in the steel reach the yield point. The horizontal arrows 2l represent the yield point stresses l'. in the steel, the arrows il the ultimate compressive stresses f'e in the concrete. This stress diagram is identical with that of a similar composite section without initial stresses in the steel. If the stress distribution was not already -balanced before the yield point in the steel was reached, it certainly will be balanced as soon as the steel begins to yield and elongation in the steel in-` 2. That due to different factors of safety applied to concrete and steel, the concrete sustains a greater part of the stresses in any composite section than is assumed in the standard design formulas.

3. That due to the difference between the stressstrain curve of the steel and that of the concrete in a' composite section, wherein the yield point of importance. With greater initial unitstresscsthe balanceotthestresseswilitakeplaceiastertban withsmallerones.

l'ig.3showsacroassectionofacompositebeam without concrete cast around the steel section. The steel section a permanently supported at bothenldscarriesitsownwsishtamitherein-4 forced concrete slab II castontopoiit. Shear reinforcement 8| intheformofananaieorother. iswelded or otherwise attachcdtothesteel beam. 'Ihe concrete slab il may have cross reintorce ment i2 ontoporbottomorboth. Theneutral axisof thecomposiiesectionilisabovcthesteel Fig.4showsacrosssectionofarectangular composite beam. steel section I permanently supported at both carries its own weight and the concrete I! cast aboutit. The concrete mayhavcthei'ormasindicatedbylinelloras indicated byline 3l. '.lheneutralaxisotthecomposits section 2l passes through the steel beam. To increase the bond between concrete and steel and'insurethetransmissionotthehorisontal shear,wiremeshorreinforcingbars8lmaybe placed around the beam, attached or not, to the Fig. 5 shows another cross-section ot a compositebeam. -Thesteel seciionl,theareaotwhich is increased by attaching a'cover plate 80 tothe bottomilangacarriesitsownweightandtheconcreteslab ii pouredontopotit. I'henentral axisofthe'compositesectionllisoutsidethecon" crete slab the steel section.

l'ilshowa thecombinationofthecomposite section with its permanent supporting members. Composite section al` is supported at its ends by pillars or the like J8 and il respectively. 'I'he live load, which the composite section is desisned to carry in addition to the dead load, is represented 40 by the vertical arrows". Unless the steel secthe steel is the determining factor for ultimate strensth, there occurs a redistribution ot the stresses between steel and concrete in favor of the steel, so that the concrete, at the moment failure starts, sustains considerably greater stresses' I than assumed in the design.

Since the concrete, partlydue to the initial stresses in the steel, sustains higher stresses from the live load than assumed-in the standard design formulas and since concrete and steel in a composite section, at the moment of ultimate load are stressed according to the actual ratio of their modulus of elasticity and th'e actual location ofthe neutral axis. it follows that any initial stress duek tothedeadloadinthesteelscctionofacomposite beam may be disregarded in the design o! said composite beam. l

'lheldead loadstresses remalninthesteelsection. but before the ultimate load is reached the distribution of the stresses in such a composite beamis exactlythe sameasinasimilarcomposite beam with effective intermediate temporary supports. Both beams, therefore, have the same fac tor of safety. This holds true for all conditions and regardless of whether the neutral axis of the composite beam is outside or inside the steel section, provided however that the concrete area and tbeshear reinforcement are designed to tabs careofahstressesduetodcadandliveload. f

'Ir'hemlsnitudeottheinitialstressesisofno tioniscamberedtooffsetthedeection due to the dcadload the composite sectionwill showa dead load deflection indicated by the broken line 4I. In addition to that the live load applied on the composite section causes a deflection shown by the brokenline.

To showthesavingobtainedbwthe useofthe present invention, one may compare thedesign with that obtained by using the prior formulas. In so doing, according to the present formula, one assumes that the dead and live loads are carriedbythe compositescctiomregardlessotthe initial stressesinthesteelproduced by the dead load. In calculating the design according to the l previously used formulasgthere is taken into consideration the initial stresses in the steeldue to the dead load. That is, it is assumed that the -steel alonecarries the dead load and that the composite section carries the live load only.

ssamm 1 Assume that a yhighway bridge is to be constructed. with strlngersections having a 8m oi' 'l5 feet, spaced feet from center to center and having a concrete slab '1.5v inches thick.,l 'Ihe bridge is to resist a moment as follows:

able fiber stress for the concrete is 1000 pounds persquareinch.

Accordingtothedesignofthepresentinvention. therequiredsteelsectionisainchwide 'plied between them.

nange section having s weight of 194 pounds per lineal toot. The section moduli o! steel and con crete ot the composite section are;

Ser-18,300 in. S|==$78 in.

The extreme fiber stresses in steel and concrete are:

Concrete, due to L.L.f,=

*WT-401.5 lbl. p01' Bq. 1li.

18000 lbs. per sq. in.

Steel, due to DL. f,'==

l f, total= 17290 lbs. per sq. in.

'9640 lbs. per sq. in.

Due to L.L. J.- -7650 lbs. per sq. in.

The extreme liber stresses in concrete and steel smi. du. m v.1..+1..i.. f.=

In aconstruetioninaccordancewiththeprlor art.therequiredsteel sectioniss llnchwide nange section having a weight ot lle pounds per lineal toot. The section moduli for the steel section and the composite section are:

y 85.7.1914 in.a S=8350 in.3 S|=305 in.l The extreme ilber stresses in steel and concrete are:

Composite sections without temporary supports.

Composito sections without temporary supports.

Concrete, due to L.L. f.=

u stesi, due to nl.. f.:

2 022,400 -l-l--- 10,200 ibs. per sq. in.

(theincreaseindeadlosdmomentisduetothe 3 28 lbs. more weight o! the steel section 114-88 (The increase in dead load moment is due to the 36 lbs.'more weight of the steel section, 230-184 lbs.)

As a result, the two bridges so designed are comparable inweight carrying capacity with a o saving in steel by the present design as follows:-

Saving per beam=2700 lbs.

The concrete slab is the same and the shear spiral about the saine for both sections. The concrete slab is the same for both designs because its dimensions are determined by other considerations. Its purpose is to provide a bridge hoor or a hoor slab in buildinss. and totran'smit upon the stringers or floor beams the loads ap- For designs made in accordance with the present invention additional concrete area will exceptionally be required.

Emmple 2 A highway bridge is constructed ot stringer sections having a span of 40 feet spaced six feet from center to center. It has a concrete slab 7.5 inches thick, and is to resist the following bending moment:

Mn.L.=1,960,000 inch pounds ML.L.=2,340,000 inch pounds The allowable extreme fiber stress for the steel.

lbs.)

'rom f.=i7,sso ibs. per sq. in.

The saving in steel by the present invention as compared with the prior art is as follows:

18 WF 114 total We1ght=40x114#=4560 lbs. 16 WF 88 wm vleightiox 88#=3520 lbs.

Saving per beam=1040 1b6.`

Theconcreteslsbisthesameandtheshearspirai about the same tor both sections.

InExampleltbesavlnginthewelghtoitbe steel in favor ci the new design amountsl to 15.65%; in Example 2 to 22.8%. The saving in cost. in per cent-of the cost oi the steel sections. is about the same. and the actual saving per beam, assuming a cost of live cents per pound of steel at bridge site is $135.00 for Example l, and $52.00 for Example 2.

There are various advantages inherent in the present invention, as ior instance in the new system 'the steel section does not have to be designed to carry alone all the dead load but it can be assumed that said loadis distributed over the entire deep section of the composite beam. It is unnecessary to use intermediate temporary supports under the beam during the pouring and setting o1 the concrete. This is of great advantage, as it increases the speed with which the structure may be erected and it decreases the cost -tnereoi substantially. Otten temporary supports are undesirable or sometimes impossible.

i'ne saving in the amount of steel not only eilects a saving in cost, butiit results in making Due to L.L. j',- 7680 lbs. per sq. in.

the complete structure lighter and results in a saving in cost of girders, columns, foundations and the like.

A composite beam, built according to the invention, has less deflection alter the concrete has set than a similar beam temporarily supported during pouring and setting ot the concrete. The' 375 lbs. per sq. in.

working stresses of the concrete at the design loadsarelowerinanunsupportedbeamthanin atemporarily supported one,asthere are,inthe rstonenostressesoronbsmallonesdueto the dead load. Itisawellknownfactthatthe plastic iiow o! concrete increases with-the increase oi the permanent compressive stress. Therefore, the plastic flow of the concrete in a temporarily supported beam must be greater than in an unsupported beam. Plasticnow may noty have great innuence on the ultimate strength of a composite beam, but it certainly increases deilection.

In the above description the invention has been applied to structures wherein steel beams were incorporated. The invention is not limited f description of which is made a part hereof.

What Iclaim is:

l. A composite steel-concrete structure com` prising a steel beam, permanent supports on which said beam is mounted, a concrete slab cast on said-steel beam, connected thereto by a shear reinforcement. said beam being deilected intermediate the ends thereof by the dead load of said concrete having been applied without temporary intermediate supports. said structure being designed to carry a predetermined deadand live load, the area of the steel section being computed on the basis that the initial stresses therein produced by the dead load are disregarded and that the composite steel-concrete section carries both the dead and live load, the area o! the concrete and the shear reinforcement being suiiicient to wiattllistand the stresses due to the dead and live lo Y 2. A composite steel-concrete structure comprising asteel beam, permanent supports on which said beam is mounted, said beam being unsupported at the intermediate portions, a con- -crete slab cast on said steel beam, connected lthereto by a shear reinforcement, said beam being deflected intermediate the ends thereof by the dead load of said concrete having been, applied without temporary intonnedii' supports, sali'ly MILL-i' MLJ..

dead and vlive load, the area of the steel section v. being computed on the basis that the 'initial stresses thereinproducedby the dead load are disregarded, theunit compressive stress inthe extreme iiber of formula Marmi' ML.L.

wherein MM" is the moment due to 4the dead load, Mm" is the moment due to the live load, and

Se is the section modulus of the concrete in com-4 pression of the composite section, the area of the concrete and the shear reinforcement being sufiicient towithstand the stresses due -to the dead and live loads.

4. The method of making a composite'steelconcrete structure designed to carry a predetermined live and dead load which comprises computing thearea of the steel section on the basis that the initial stresses therein produced by the dead load are disregarded, supporting said steel section on permanent supports without temporary intermediate supports, pouring concrete on said beam without `the presence of temporary intermediate supports, and allowing said concrete to set.

5. 'ihe method of making a composite steelconcrete structure designed to carry a predetermined live and dead load which comprises computing the area of the steel section on the basis that the initial stresses therein produced by the dead load are disregarded, the unit tensile stress in the extreme liber of the steel being based on wherein HD. is the moment due to the dead y loadJl L isthemomentduetothelivelomand B. is section modulus of the steel section ot -thecompositesectiomtheareaoftheconcrete andtheshearreinforeementbeingsuiiicientto withstand vthe stresses due to .the dead and live loads.

3. A composite steel-concrete structure comprisingasteelbeam.permanentsupportson whichsaisibeamismounted,saidbearnbeixig` unsupportedatitheintermediateportions,acon-A the formula MD.L.+ML.L. S.

S. is Ithe section modulus of the steel section ot the composite section, supporting said steel section on permanent supports without temporary intermediate supports, pouring concrete on said beam without the presence of temporaryv intermediate supports, and allowing said concrete to 6. The method of making a composite steelconcrete structure designed to carry a predetermined live and dead load which comprises computing the size of the steel section on the basis that the initial stresses therein produced by the deadload are disregarded, supporting said steel section on permanent supports without temporary intermediate supports computing the area of the concrete section on the basis that the composite steel-concrete section carries both the dead and live load, pouring concrete on said beam without the presence of temporary intermediate supports, and allowing said concrete to set.

'1. The method of making a composite steelconcrete structure designed to carry a predetermined live and dead load which comprises compitting the area' of the steel section on the basis that the initial stresses therein produced by the dead load are disregardedth'e unit tensile stress in the extreme fiber of the concrete being based on the formula MmLEFMLL.

the concrete being based on the assenso wherein Limb is the moment dus to the dead load, um is the moment due to the live load. and Se is the section modulus of the concrete in compression o! the composite section, supporting said steel section on permanent supports without tem porary intermediate supports. pouring concrete on said beam without the presence o! temporary intermediate supports, and allowing said ooncrete to set. Y

8. A composite steer-concrete structure comprising a steel beam, permanent supports on which said beam is mounted, said beam being unsupported at the intermediate portions, concrete cast about said beam to provide a unitary structure, said beam being deflected intermediate the ends thereoi.I by the dead load of said concrete having been applied without temporary intermediate supports, said structure beingdesigned to carry a predetermined dead and live load, the area of the steel section being computed on the basis that the initial stresses therein produced by the dead load are disregarded and that the composite steel-concrete section carries both the dead and live load, the area of the concrete and the shear reinforcement being suillcient to withstand the stresses due to the dead and live loads.

9 A composite steel-concrete structure comprising a steel beam. permanent supports on which said beam is mounted, said beam being unsupported at the intermediate portions, concrete cast about said beam to provide a unitary structure, said beam being deflected intermediate the ends thereof by the dead load of said concrete having been applied without temporary intermediate supports, said structure being designed to carry a predetermined dead and live load, the area of the steel section being computed on the basis `that the initial stresses therein produced by the dead load are disregarded, the unit tensile stress in the extreme liber of the steel being based on the formula loads.

' CLEMENB PAUL CUIN'I.

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