Question

Draw the shear and moment diagrams of the beams without obtaining equations. After determining the elasticity equations of the beam shown, draw the deflection curve

1.5 k/ft 30 k A с 6 ft BE + 4ft - +5ft- El = constant E = 1,500 ksi I = 20,000 in.4 mind

Answer 1

30k 1.5k/ft AM B K "ARB=79.5k 9ft oft -40-SK = EI = constant E = 1500 ksi I = 20000 in Stepi- Obtain suport reaction EMAO, (15*6XE) - (Rems) + (30 %&+6)] = 0 [PB = - 79.5 K EFy0 RA+RB -(1:5*6) - 30 = 0 => [RA: -4o5 K • Step2 - Drawing SFD. Зоk Зок A B с -40.SK a end gives 249.5k Step3 Doawing BMD- Area of SED at upto a desio ed secth foom B.M at that particular sect". B.M at A due is zero because pin end B.M at C is zero because foee end B.M at B is, Adea of SFD from A to B. Ź (440.5)+49.5)) * 6 = -270k-ft 6 . B.MO

B! • straight 2 cuove BMD. 270 koff Step 4. Elastic curve eqn. EI d'y da² - Mc. a 30K 1.5k/ft 3 A mongo 40.5k 79.5k SC {Max * 640.5x) +(-1*5*6* (***X-2)) +(79-5*(x-6)) = My Erdby,= (-40-5x) (+{*5*6(x-2) +(79-62<x>0}} + cntigrate above. to get slope equ. Eidy da (-40-52°)+4 + [11586(X=9397]4 (79526x2-03] slope equ. intigrate slope ear to get difffection equ. ETY - (20.5x)+Cx+44 ( 15 ( 3*]|[735*[***] Deflection equi

Step 5- Deflection curve. Deflected shape.of beam. Note. Since the BMD.ch -ve adeo all over the beam moment deflect the beam is in Hogging shope sol Hogging 0