rN! PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES retum on or before date due. DATE DUE DATE DUE DATE DUE | — SES MSU Is An Affirmative Action/E qual Opportuntty Institution nse. -: THESIS :- TESTS OF STEEL-CONCRETEHE BEAMS. BY ~ C. M. BLANCHARD ©n, W. C. ARMSTRONG. Class '03, THESIS TESTS OF STEEL-CONCRETE BEAMS, The object of this set of tests was to determine how well the results obtained by means of the theory proposed by W. Kendrick Hatt, of Purdue University would agree with the results obtained by tests made on beams which were of varied proportions of matrix and aggregate and of the reinforcing material and which were also maie unier varied conditions, Tne beams used in these tests were made in wooden moulds. Those marked dry and normal in Table I. being thoroughly tamped, while those marked very wet were tanped but little. Tne >eans were oc a uniform size, all being six (6) inches square end of sufficient length to give a span of sevejzty-two (72) incnes between supports, except beams 52 and 5b which ned a span of thirty-six (36) inches. The reinforcing material useli consisted of Be and 14" round rods of mild steel and were aj] placed 1" from tension face of beam, two being used in eacn beam, 34084 Two differert brands of cement were used (Atlas and Aetna). the Atlas being a well known svandard brand, and the Aetna, a local cement which is made at Fenton, Michigan, Tests of standard bri- quetvtves were :nade on both cements, the results being shown in Table IV, All beems were made indoors and were left there until taken from moulds, which time varied from one to four days accorlin.: to tne amount of water used in mixing, after which they were set out doors until tested. Beams were all of gravel concrete, As sand wes in excess, the gravel was &11 sifted through a sieve of sixteen meshes to the square inch, all stones larger tha: 1," inch in iilaneter being rejected, then the sand passing through the sieve and the stones cauzht by it were mixed with the cement in the ratios (by volumes) as gnown in Tahle I, The beams were tested at azes varying from 7 to 64 days as shown ix Tale II. All of the beans were broken by meens of the Tinurs Olsen testing machine in the Meshanical Laboratory, wnich the elastic lirit of the reinforcing metal is reeched, he calls this point the point of failure, But, as all the beams in these tests failed by crushins of the concrete instead of by breaking of the rods, the theory proposed by him would hardly apply at the point of failure for these beans, Wo curves were plotted for beams Sa end 56 whicn were of plain concrete without reinforcement es the totel deflection for either wes less than .Q1 of an inch, and the only value of the tests of these two is to stow to whet s marked degree tne flexibility of tne beams is increased py tne addition of the metal reinforceme:t, The assumptions uoon which the theory proposed by Mr, Hatt are based are as follows; 1, The cross sections of the beams remain plain surfaces; 2. Tue applied forces are serpendicular to the neutral surface of the beam; 3, The values of the moduli of elasticity obtained in simple tension and comoression tests will apply to the material in the beans when under flexion; 4, There is no slipping vcetween the concrete end the reinforcing metal; 5, There are 10 initial stresses in the beam due to cortraction of tne concrete (4) While settinz, The analysis also sucroses the fracture to be due to bending and not horizontal shear. If the cross sections are assumed to remain plain surfaces during flexture the distortion of any fibre wil? be provortional to its distance from the neutral axis, It follows that the law of variation of stresses will be represented hy the stress strain diagram shown on curve sheets. ‘These stress strain diasrams are assumed to be parabolic arcs, This assumption has becn justified in the case of compressional stress strain dia- diagram, by a large number of experinents but does not seem to be so clearly shown in this case, The quantities used in the formulas for tneoretical results were as follows: it hx distance from compression face to neutral axis. hu il distance from compression face to the center of gravity of the reinforcement, } p <= ratio of area of steel to tnat of cross section of beem, Es, Ec, Et = moduli of elacity of the steel, concrete in com- 7 >ress3ion and concrete tension, respectively. Ee n = Et . 2S m © Bt f = stress in metal reinforcement, (5) it c = comvression stress in outer fibre of concrete, t = tensional stree in outer fibre of concrete assumed to be 300#. Ec and Et are measured at tne stresses c and t. The values x, u and p are ratios; p and u are at the control of the designer, while x depends on p, u, n and m3;.n and m are fixed by the quality of the materisls, and they chan:ze during flexure with varying values of c, f and t; that is, the modulus of elasticity of the concrete varies with the stress at which it is measured, For practical purposes of computation, however, the constant values of n ard mirsy ve used appropriate to the point A and to tne point of cracking, The values proposed by Prof, Hatt were N= 2 and m—12 at point A, and n=12 and m= 90 at point of first crack, and these values were used in computing the results shown in Table III. On the assumption of plane cross section during flexure we mey determine the ratio of f to c and f to t in the following formulas tnx Cc =-T—x r- tm(u— x) il—x Next, to locate the neutral axis; ie, to determine the value (6) of x, we mey ecuete the forces of tersion amd somoression on the cross section, asswsins, a3 before, t.int the streas strain diagrams are arcs of parabolas, £4 ex—*% t(1 — x)+ pf into which the values of f and c above may be substituted and, solving for x, we get 24 x*n="/ (1 — x)*&4 pm(u — x) and, after solving, this reduces to x= -(4,5)4 “Yan + 5° m + p [6m(u[n — 1)+ 1)) e(n— 1) Havin:: obtained x we may compute c and f and finally obtain tne moment of resistance of the section, Taking moments about the neutral axis, we have ee pnx” (n — x)* w= tfh [a (1 — xF + re pp maa] These equations are to be applied to compute the load at point A, At the load corresporndin,s to the crackins of the concrete in the tension face, these equations should be modified to corres- pong to tne fact that tne stress strein aiagram for the concrete in tension is more nearly a rectaigle than ea parabola, The differci:c ., nowever, vevween iene results at the time of the appearance of the (7) crack due to the assumption of a rectansle or a perandola is very small, With proper values of n and m the equations may be allowed to sterd. When, however, the creck heving formed itself, extends throughout the lower region of the cross section the equations must be modified by the omission of tne effect of tensional forces due to the resistance of concrete under tension, We then have: nox = pf or p Su —-x)= Sx? which serves to locate tire neutral axis, The loéds combuted by the application of tine forezoing equations are shown in Table III and are to be compared with those piven in Table II, which are tne loads carried by the been tested. From an inspection of Tavle II, it may be seen that both the point A, and point of first crack varied considerably for tne different beams, but this would be expected, as the beams were vur- posely made with as meny varying conditions es possible, The ratio of the greatest to the least value of A Was as 3:1, and for the voint of first crack less than 2:1, ana dota cases the theoretical load was a mean between the two, therefore we may conclude that with a large fa ctor of safety, such as is (3) necessarily used in concrete construction due to the fact that two pieces of concrete made uuder sinilar conditions, do not show concordant tests, it would be yractical to use these formulas with the constants here employed for tne design of concrete steel beams, (9) Kind, TABLA NO, I. Condition A 4a \When made, , After Test, Wee los, No, No. No, No. 5e ard 5h No, No, No, No, No. No. No, Wo. No, No, No. 1. 10. ll. 12, 13. 14, 15. 16. O:3:1 Aetna " n " " 3:2:1 Atlas " n S3se:l1 Aetna tt n 3:231 Atlas " " 4:2:1 " Sre:l " " " Biel " " n S:2:1 Aetna i" " — + -_ - 2. Rether dry First cracked on bottom then crumbl- 250 ed on top. " " Same as No. 1., Also slivered along rods, 206 " " Crushed on bottom crumbled on top, O28 " " Cracked on »otvvon crumoled on too, 250 " " Cracked clear tnrouzh a - 113 glad not crusa. b- lol Normal Crecked on bottom then crusned on top, 204 " Cracked on bottom vhen crusi:ed on tor, el Very wet Split alonz rods on hnoalf of beam,. : 259 " " Split alonz roads on nealf of beam, 260 " " Cracked on Lotrtom tien crus‘ied on top. 209 " " Split alon= rods on helf of beem, LOS " " Cracked on bottom tien crus:ed on ton, 2 46 " " Cracked on bottom then crushed on top anda sli- 267 vered short dis, on side " " Cracked on bottom cruyvi- led on top ctnen broke 267 out chunck on bottom Normal Cracked on vottom crush- ed on top then cracked 255 diasonelly across beam " Broke neerly strait 299 across, (10) TADLE NO. II. Point A, Crack, Failure, Bean Kina. Age in Loed Defl. Load | Defl., Load Defl, No. Days. oounds! inches vounds'inches pounds incnes 1. 61% 7 1,000 0.12 2,000 0.40 2,100 0.75 2. 61% 64 600 0.05 2,800 0.38 $3,000 0,75 3. «61% 64 600 0.05 2,800 0.38 3,000 0.75 4, .61% 28 1,000 0.08 --~---- ~~-- 2,500 0.82 5a, Plein 28. ----- e--- o---- ---- 1,500 0.0068 5b. " £8 9 =nene ean a---- ames 1,300 0,01 6. ~ 61% 31 1,200 0.04 38,400 0.35 38,600 0.90 7. .61% 31 800 0.03 3,200 0.30 3,600 0.74 8, 1.09% 34 9 a--5- ---- 1,800 0.20 2,000 0.41 9. 61% 34 400 0.02 2,200 0.28 2,100 0.32 10. 1,09% 29 600 0.01 1,800 0.19 2,000 0.27 11, 1.09% 29. 1,000 0.12 1,600 0.22 1,800 0.27 12. 1.09% 29 400 0.04 1,800 0,24 2,000 0.£8 13, 1.09% 29 1,000 0.07 3,000 0.29 3,800 0,45 14, 1.09 29 1,000 0.08 2,800 0.28 3,400 0.48 15. 1.09% 25 1,200 0.08 2,200 0.24 2,800 0.49 16, .61% 25 1,200 0.03 2,000 0.18 3,000 0.38 - Se © eee ee ee OO - -e *" ba abd Ob 3' between supoorts, (11) TARL:: NO. III. Stress per Concrete in Rein- Loed at sq. in, steel. Comp. Value of x for forced Point First Point First Point First Point First per cent A. Crack. Moment due to weight of Beam to be deduced from theoretical dead loads. TABLE NO. IV. Tensile Strenzth of Standard Briquettes of Atlas Portland Cement, Neat, 7 days. el days. " §24 | 640 " O14 622 " 475 635 504.35 6a50