THE STRENGTH OF FILLER JOIST FLOORS.-By Ewart S. Andrews, B.Sc. En@, M.I.Struct. E., A.M.1nst. C.E

ANY structural engineers have for a M long time been convinced that the effect of casing steel beams in concrete in the manner which has obtained for many years with the filler-joist floor, has a

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strengthening effect upon the floor and that it is safe to design the steelwork in such floors upon higher stresses than the ex- treme fibre stress of 7.5 tons per square inch which is usually specified.

Some designers have followed the rule of taking the stress up to IO tons per square

inch (an increase in strength of 33 per cent.), but up to the present there has been but little published of experimental tests upon which we could base a demand to have the specifications and bye-laws re- vised so as to enable us to design the steel- work for such floors more economically.

In many cases the filler-joist type of floor has considerable advantages; it is quick in construction and avoids the trouble atten- dant upon supporting centering from below ; moreover, the ordinary compara- tively small builder, who perhaps has not on his staff any men who have had suffi- cient knowledge and experience for ordinary reinforced concrete work, can undertake th i s kind of floor satisfactorily.

I t is, therefore, with great interest that we have studied the report just published by Messrs. Redpath, Brown & Co., Ltd., on the " Strength of Steel Joists Embedded in a Solid Concrete Floor Slab."

The report, which is prepared by Mr2 J . R. Sharman, M .Inst .C .E ., describes the results upon tests made at the National Physical Laboratory upon a machine which was designed by Mr. Sharman, in consultation with Mr. J. Mitchell Moncrieff, C.B.E., hl.I~:st.C.E., M .I .Struct.E ., to deal with tests upon horizontal and vertical specimens, and was presented by Messrs. Redpath, Brown OL Co., Ltd., to the National Physical Laboratory.

SCOPE AND METHOD OF TEST. Two series of tests were made- I . With 4 x 19 R..S.J. 9 ft. span. 2 . With 6 x 3 R.S.J. 14 ft. span. Frames were made with two tie-bolts in

the length and were tested plain ; similar frames filled with concrete flush on the bottom sides and of the various depths shown in Fig. I were also tested.

A similar frame with concrete flush top and bottom was also tested, but the -report states that this showed little gain of strength

THE STRUCTURAL ENGINEER. 39

over the plain joists, and is not included in the table accompanying the report ; we refer to this in greater detail later.

L 3.3 -

A The method of testing was as follows :-

T h e load was applied over the whole width of the slabs, either at the centre or at two points and diagrams were made of the de- flections plotted against the loads; the diagrams indicated clearly the limit of pro- portionality where the straight line com- menced to curve away and the loads at these elastic limit points were called the test loads and were reduced in every case to equivalent uniformly distributed loads.

The report states that " the concrete was composed of 4 parts Thames gravel, 2 parts of sand to I part of cement, mixed in the ordinary way, worked between the joists of the frames with a shovel and then levelled off. No special precautions were taken, with the idea of reproducing the conditions of work on an ordinary building contract. Tests of concrete cubes and cylinders made at the same time 'as the floors have an average crushing strength of only 1,443 lbs. per sq. inch and an average modulus of elasticity of 1,250,000, showing the con- crete to be below average quality. This, however, did not materially affect the strength of the slabs.

We refer to this point later. SUMMARY OF RESULTS.

% decrease in de- flection due to con-

increased load). crete (in spite of

T h e calculated stress in the plain joists at the test-load (practically the elastic-limit load) was 13.8 tons per sq. in. for the 4 X 19 beams and 12.1 tons per sq. in. for' the 6 x 3 beams, the ultimate strength of the material in the two cases being 29 and 28 tons per sq. inch respectively.

These comparatively low results seem to show that buckling of the compression flange was the cause of failure, as it usually is in beams without lateral support; the ratio of span to breadth of flange for the two cases was 62 and 56 respectively.

Extensometer tests, giving the actual tension in the bottom flange of the R.S.J. and compression in the concrete, were taken for specimens J, K and L. At the limit of proportionality the tension in the steel averaged for the three slabs was 15.2 tons per sq. in., and the compression in the con- crete 920 lbs. per sq. in.

In regard to deflection, it should be noted that the concrete slabs are much stiffer than the plain joists. Although carrying heavier loads, the deflection of the concrete slabs is approximately only half that of the plain joists.

COMPARISON OF RESULTS WITH THEORY.

Mr. Sharman states that " by calculation similar slabs, made with concrete having a crushing strength of 2,400 lbs. per sq. in. and a modulus of z,ooo,ooo indicate an in- crease of only about 5 per cent. in the load carried before a similar stress would be reached in the steel.

W e think that Mr. Sharman must have based his calculations upon the theory of reinforced concrete slabs which assume the steel as concentrated at its centre and takes no account of the depth of the steel, and not upon the theory which we have advocated for many years.

As the latter theory does not appear to be very well understood it may be of interest to work out in detail one of the cases tested and to give the results of all the others.

We will take case L , in which we have 6 x 3 I beams at 2 ft. 9 in. centres and con-

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40 THE STRUCTURAL ENGINEER: The Journal -~ ~

crete 2 in. above the top flange.

stress diagram. Fig. 2 illustrates this, together with the

In this method we first find the neutr axis by the ordinary formula for reinforced concrete beams, viz. :-

b n2 - = m A (d-n) ... 2 ... ( l )

we take m = 15, and for the 6 x 3 I beam A = 3.55 . * . inserting our values from Fig. 2 we have

2 33n: = 15 x 3.53 (5-11)

16.511~ = 26S-S3n n 2 + 3 - 2 1 n - 1 6 - 1 = 0

n = - 3 - 2 1 + 2 / 3 - 2 1 2 + 64.6

2 = - 3.21 + 8.65

= 2 - 7 2 in. 2

The above formula can be solved by means of the diagram Fig. 3, which gives

results for various percentages o f rcinforce- ment ; the diagrams usually given do not extend sufficiently far to deal with the pre- sent cases in which the percentage of re- inforcement is higher than in ordinary re- inforced concrete design. In our case the

% reinforcement is 253 ~~ x 100=2 - 14,

and from the diagram - = -545, so that

n = -545 X 5 = 2.72 in, We next find the equivalent moment of

inertia (IE) of the section about th i s neutral axis of the formula

33 x 5 n d

bn3 I E =-

3 + m (I, + A (d - n2)

where IB = moment of inertia of steel beam about its own N.A. - - 33 x 2*723+ 1S (20-2 + 3 - 5 3 ~ 2 . 2 8 ~

3 = 221 + l 5 X 38.5 = 798 inch units.

This if BC and Bs are the safe bending moments in inch pounds which will induce stresses of c in the concrete in compression and t in the steel in tension, we have for c = 600 and t = 16,000.

- "' x 798 = 176,000 in.-lb. 2.72

- - 16'ooo . __ 798 = 161,000 in.-lb. IS 5 - 2 8

For the I beam alone we have 16,000 X 20.2

3 B ~~__.__.____

(20 -2 being the moment of inertia and 3 the half depth),

= 108,000 in - lb. . . Increase due to casing = 161,000 -

108,000 = 53,000, . . x increase in strength due to casing =

-_ 108 3 J x l00 = 49.

of THE INSTITUTION OF STRUCTURAL ENGINEEKS. 41

The test result was 38 per cent. increase. The following table gives a comparison

between the results of the tests and of the above theoretical treatment for the various cases.

% increase in strength. Mark. - I Bv Theorv. l Bv Test. D 60

38 29 J 140 90 F

40

L 49 38 K 79 l 85

l i

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On the whole this comparison shows a fair agreement between theory and practice, and although Mr. Sharman thinks that the IOW strength of the concrete did not materi- ally affect the strength of the slabs, we believe that the results would have been higher had the concrete been of the usual strength.

COMMENT UPON RESULTS.

It should be noted that the results given are for the increase of load for the elastic limit as determined by the deflection measurements, and no record is given as to the relative ultimate strength of the speci- mens.

This brings us to a point upon which there is a wide difference of opinion among engineers; we believe that those engineers who have most experience of experimental work are agreed that it is, on the whole, best to base working stresses upon the elastic limit, but the factor of safety that one adopts should depend upon the ratio of the elastic limit to the ultimate strength. That is why we use a lower basis stress for compression members than for tension members (usually 6.5 and 7.5 tons per sq. in. for mild steel).

Although, therefore, we think that the elastic limit strength is of great importance, we think that the ultimate strength should also be considered. No figures as to these rrltimate strengths are given in the report.

We expect, however, that if the tests were

carried to the practical failure point-say the point at which the deflection became 5 in.-then the uncased joists would show considerably lower strength than those cased flush top and bottom. We think also that the relative increases of strength for the other cases would be higher if the prac- tical failure load were taken instead of the elastic limit load.

At some later date, perhaps, the load- deflection diagrams will be published, and we shall then be able to have an interesting discussion of them and shall probably be able to learn much from them.

In many respects it is a pity that the con- crete was clearly below par in quality, but it is reassuring that even with poor concrete the increased strength due to the casing was so great.

There is one point which we do not follow from the report, but which is of importance for the true interpretation of the results; that is the manner in which the weight of the concrete casing itself has been taken into account. If it should transpire that the loads given are the superimposed loads, then it is clear that the relative strengths for cased and plain beams are really higher than the figures given.

We hope this research work will be con- tinued; there are many moot points in the design of structural steelwork that can only be settled by experiment. We believe that there are many directions in which econo- mies in design could be effected if we had the experimental evidence which would enable us to design upon sure knowledge, and thus to reduce that child of ignorance that we call the Factor of Safety.

It is quite clear that sufficient evidence has now been collected to show that a con- crete casing has a marked effect in increas- ing the strength of structural steelwork; and we should see to it that those who %it on the local authorities over us shall make suitable revision in the official regulations that hamper efficient design and make steel structures cost more than they need.