Question

For the beam and loading shown, please (a) determine the reactions at A and C, (b) draw the shear and bending moment diagrams, and (c) find the maximum normal stress on the beam.

2000 lb 200 lb/ft 4 ft 4 ft 6 ft

Answer 1

Questions Given data & 2000 16 200 lblft K 4ft kaft 6Ft solution & @ Reaction at A ando Let .RA= Reaction at A RB = Reaction at a p upward Reaction ④ v down ward reaction ③ 2000 lb 200 lblft I ctttto le 4 ftt 4 ftote oft TRC D

& Efv=o c sum of all vertical Forre&zo) 9 RA - Rooo + Ra - Cook6) = 0 - [RA + Rc= 3200 16 0 > {ma=O (Bending moment about = ( Rex 8) - [ 200X6X(6 +8)] - (2000X4) = 0 Azo) > 8 Rc = 21200 - TRC= 2650 16 from equation ® = RA = 32 oo – R8 = 550 45

lb π RA= 550 Rc = 2650 lb 2000 16 200161 Ft Aft k 6ft Kart 550 1b 265016 ② Bending shear force and moment diagrama * Shear force calculation & » © At © At D VA = 550 16 a VD = 550 -2000 = -1450 16 V © At C Vc = -1950 +2650 ve = 120016 + Vg= 1200 -(200x6)=0 at @ At B I end

e shear force diagram 1200 16 55016 55016 O ve .- 1450 lb - 1450 lb maximum. Shear force . = 1450 16 C magnitude)

* Bending moment calculation & O AT A @ At D MAZO lb-ft mo = (550x4) = 8200 16- Ft mes (550x8) - (2000xY) = -3600 16- Ft * At c @ At B mies (ssorius - (Qoosx 10) + (2650x6] -(200X6x3] MB= o lb-ft - - maximum maximum ② ve ☺ ve moment = 2200 18-ft moment = 3600 lb-ft a (M Đ velm =2200 18-ft cm ve) max = 3600 16-64 magnitude wise may = 3600 lb-ft

olo - Bending moment diagram 2200 lb-ft A-PARABOLIC 3 600 lb-ft

maximum normal stress og By apply Bending equation | مه M= Bending moment (maximum) I= moment of Inertia o= maximum bending or normal stress 2 = کرا section modulus - 4 in köy y=8 in - in this case T= 4x 8 min z = 4x8? = 42.67 inch L = 2 = 42.67 inchal

maximum Tensile normal stre88 88 (By taking M ove) (ot) max = M 42.67 m. ve = 2200 16-Ft 22008 12 M = 26400 lb-in - Cot) may 3 86400 - 618.70 psi - 42.67 = 0.618 Ksi = (Ptmax=0.618ksi - Tensile ® maximum compressive normal stress ( By taking m ove] * Move = 3600 16- Ft= 43200 18-19 lift = 12 10 ) I'M = 43200 lb-in

___ ) Smax E - 43200 ५३.67 | 102 1 42 Ps | Gmix = 162 ksi

.: maximum hormal stress - (०३,५२ Psi : = 1,018 Ksi (Compressive]