Page 429. Sample Problem 6.2.Solve the problem completely;but this time,placethe three applied forces from2.5 kips, 1 kip and 2.5 kips to the new values 3 kips, 2 kipsand1kip.Keep in mind that this change will result inmany other changes across the board.Discuss all practical issues in your findings 2.5 kipsс3 kips(6)-2--3--3--2-3 kips6 kip-ftb-3.5 in.3.5 in.1 kip-0.5 kipI(1.5)DI--411.25 in2.5 kipsFig. 2 Section ofbeam having depth d05 kip(-1.5)7.5 kip-ftEFig. 1 Free-body diagram of beam withshear and bending moment diagrams.(-6)3 kips6 kip-ft4 in. x 12 in.nominal sizeFig. 3 Design cross section.MODELING:Maximum Shear and Bending Moment. The free-body diagram isused to determine the reactions and draw the shear and bending-moment dia-grams in Fig. 1. We note thatANALYSIS:**Design Based on Allowable Normal Stress. We first express the elas-tic section modulus S in terms of the depth d (Fig. 2). We have-3 kips1=hd¹ S====bd² = (3.5)d² = 0.5833d²MS=T=VFor Mx = 90 kip-in. and = 1800 psi, we write3 V2 AMd² = 85.7= 7.5 kip-ft = 90 kip-in.= 3 kipsWe have satisfied the requirement that ≤ 1800 psi.Check Shearing Stress. For Vx = 3 kips and d = 9.26 in., we find0.5833d²===90 x 10' lb-in.1800 psid = 9.26 in.3 3000 lb2 (3.5 in.) (9.26 in.)3 V2 ASince = 120 psi, the depth d= 9.26 in. is not acceptable and we mustredesign the beam on the basis of the requirement that T ≤ 120 psi.Design Based on Allowable Shearing Stress. Since we now knowthat the allowable shearing stress controls the design, we writeT = 138.8 psi120 psi3 3000 lb2 (3.5 in.)dd = 10.71 in. 4The normal stress is, of course, less than = 1800 psi, and the depth of10.71 in. is fully acceptable.REFLECT and THINK: Since timber is normally available in nominaldepth increments of 2 in., a 4 x 12-in. standard size timber should be used.The actual cross section would then be 3.5 x 11.25 in. (Fig. 3). 2.5 kips 1 kip2.5 kips2 ft 3 ft 3 ft2-10 ft-Sample Problem 6.23.5 in.BA timber beam AB of span 10 ft and nominal width 4 in. (actual width =3.5 in.) is to support the three concentrated loads shown. Knowing thatfor the grade of timber used all = 1800 psi and Tall = 120 psi, determinethe minimum required depth d of the beam.STRATEGY: A free-body diagram with the shear and bending-momentdiagrams is used to determine the maximum shear and bending moment.The resulting design must satisfy both allowable stresses. Start byassuming that one allowable stress criterion governs, and solve for therequired depth d. Then use this depth with the other criterion to deter-mine if it is also satisfied. If this stress is greater than the allowable,revise the design using the second criterion.(continued)

Question

Accepted Answer

The forces 2.5kpis, 1 kip, 2.5kips are replaced by 3kips, 2kips, 1 kip respectively.
For timber…