Question

A simply supported beam has a cross section of 2 in. wide by 6 in. tall. It is loaded by two vertical 8,000 lb forces acting at 4 ft from the ends of the beam.

a.)    Determine the maximum bending stress, psi, in the beam

b.)    Determine the maximum transverse shear stress, in psi, in the beam

Cross section 8,000 lb 8,000 16 bh3 12 II 4 feet 6 feet 4 feet 2 inches

Answer 1

simply supported beam and loading condition is shown below:- svoolb swolb T Gin А c D 1 RAL 4ft ok 6ft 4 ft B kain from symmetricity stepi- I. Calculation of support reaction:- RA= Rp= 8coolbl l upwand, Step: Bending moment catew ation: Bendling moment (B.M.) at x b/w A ando B.M. & RAX swolba 8 wore lb.ft. B.M. b/w C 4D B.M. = 8 voox. 8w0(3-4) - 32000 lbift: B.M. b/w Doard B. B.M. fwo (3-4) - Gwo (6-10) 2 8wox- swox + 32oo - fwox t 8000 2 800ox- foox + 112,00 Step. II. calentation of moment of Prestian & Area, 12 I bd 2inx(sing 36 int X 12 12 Area (A)= bd 2 inx bin 2 in x Gin & 12 in2 Step. D. Drow Bending moment dia diagram and shear S.A.D.) sign for S.R.D. a 1 the sign for B.M.D. = 8 +5 force diagram. (sf.

swolb froolb. B D. katt oft - eft sikisi + 8vo IL А R & wolbi B.M.D. 81002 32wol bitt + + B clearely Maxim Bending nument (Mmox) = 32wo Ibitt. 2.32000/bi(12inch) 3 384 000 lb. inch, sheen firce (Vmax) = 8 000 lb. Main Rending chess occur at section where Boneling moment is main and at extreme fibre, M Omar x Binch, 32wo pri Ani 384 no lb. inch 36 int (b) Max shear stress will occur at section where shear free is may and at Neutral Axis. Became magn shen stress is Tmare A 1.5 times our shem stress 8oolb 1000 pst Ansi Zmara * 15 12 in 2