Maximum Stresses in BeamsWhen solving the problems for Section 8.4, consider only the in-planestresses and disregard the weights of the beamsProblem 8.4-1A cantilever beam of rectangular cross section is subjectedto a concentrated load P±17 k acting at the free end (see figure). The beamhas width b±3 in. and height h±12 in. Point Ais located at distancec±2.5 ft from the free end and distance d±9 in. from the bottom ofthe beam.Calculate the principal stresses s1and s2and the maximum shear stresstmaxat point A. Show these stresses on sketches of properly oriented elements.Probs. 8.4-1 and 8.4-2PcAbdhSolution 8.4-1P±17 kc±2.5 ftb±3 in.d±9 in.h±12 in.v±0.3STRESS AT POINTAI±432 in.4M±²PcM5.1³105lb-in.V±PV±1.7³104lbyA±3 in.sx±3.542³103psiQ±40.5 in.3t±531.25 psitxy±tsx±3.542³103psisy±0txy±531.25 psiPRINCIPAL STRESSESup±8.35 degup±12atana2txysx²sybtan12up2±2txysx²sy±2txysx²sy±0.3t±VQIbQ±bd
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