Question

Question 3 Use Moment Area theorems in the beam shown in Figure 3 to determine the following: a- Deflection at C. b- Deflection at D. C- Slope at C. d- Slope at D. Use E for modulus of elasticity and I for moment of inertia for the whole beam.

Answer 1

Basically we need bith slope and deflection at C and D

to find deflection , we need slope first

slope is given as= area of mending moment diagram/EI

delflection= slope *L , where L= distance between point of deflection and cetre of gravity of the Bending moment diagram.

and deflection at C is = (106.56/EI)*(32/3) =1136.64/EI, (for triangle CG lies at h/3 from base)

similarly for point D,

slope at D =area of bmd(triangle EGD)/EI =((1/2)*(4+3.33)*(40)) /EI =146.6/EI

and deflection at D =(slope at D) *40/3 =1954.67/EI (for triangle EGD cg lies at 40/3 from base)

for any doubt aske me in comments .