Homework2

1. Pb.1 # Find deflection, shear and moment distribution 1𝐸𝐼𝑉′′′′ = 0 2𝐸𝐼𝑉′′′ = 𝐶1 3𝐸𝐼𝑉′′ = 𝐶1 𝑋 + 𝐶2 𝐸𝐼𝑉′ = 𝐶1 𝑋2 2 + 𝐶2 𝑋 + 𝐶3 4 𝐸𝐼𝑉 = 𝐶1 𝑋3 6 + 𝐶2 𝑋2 2 + 𝐶3 𝑋 + 𝐶4 5

2. B.CS At X=0 V (0) = 0 𝑉′ (0) = 0 At x=L V (L) = 𝛿 M (L) =0 Substituting B.CS in equations 2,3,4,5 we get i𝐶1 = −3𝐸𝐼𝛿 𝐿3 ii𝐶2 = 3𝐸𝐼𝛿 𝐿2 𝑉( 𝑥) = −3𝛿 6𝐿3 𝑋3 + 3𝛿 2𝐿2 𝑋2 𝑀( 𝑥) = −3𝐸𝐼𝛿 𝐿3 𝑋 + 3𝐸𝐼𝛿 𝐿2 𝑆 ( 𝑥) = −3𝐸𝐼𝛿 𝐿3