Pb.1

# Find deflection, shear and moment distribution

1 𝐸𝐼𝑉′′′′ = 0

2 𝐸𝐼𝑉′′′ = 𝐶1

3 𝐸𝐼𝑉′′ = 𝐶1𝑋 + 𝐶2

𝐸𝐼𝑉′ = 𝐶1𝑋2

2+ 𝐶2𝑋 + 𝐶3

4

𝐸𝐼𝑉 = 𝐶1𝑋3

6+ 𝐶2

𝑋2

2+ 𝐶3𝑋 + 𝐶4 5

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

i 𝐶1 =−3𝐸𝐼𝛿

𝐿3

ii 𝐶2 =3𝐸𝐼𝛿

𝐿2

𝑉(𝑥) =−3𝛿

6𝐿3 𝑋3 + 3𝛿

2𝐿2 𝑋2

𝑀(𝑥) =−3𝐸𝐼𝛿

𝐿3 𝑋 +3𝐸𝐼𝛿

𝐿2

𝑆 (𝑥) =−3𝐸𝐼𝛿

𝐿3