Question

Problem 2 A torque is applicd to the two material bar shown. (The materials are bonded tightly together.) a) Calculate the torque carried by cach material b) Caiculate the angle of rotation of the bar at point B, mid-way along its length. c) Calculate the maximum shearing stress for each material d 10 mo a bleere) o.Sm G= 14 G G8 G T S0 N.M Th 2

Answer 1

Part a

J₁ = (/32) * 10⁴ = 981.75 mm⁴

71

J₂ = (/32) * (15⁴ - 10⁴) = 3988.35 mm⁴

71

Torque resisted by materials 1 and 2 = T₁ and T₂

Angle of twist _{= $\theta$1} = _$\theta$2

(T₁L₁/G₁J₁) = (T₂L₂/G₂J₂)

Given L_{1 =} L₂

T₁ = (G₁J₁/G₂J₂) * T₂

G₁ = 14*10³ N/mm²

G₂ = 8*10³ N/mm²

T₁ = (14*10³/8*10³) *(981.75/3988.35) * T₂

T₁ = 0.431T_{2 Eq 1}

T₁ + T₂ = T = 50000 N-mm   _{Eq 2}

Equating equations 1 and 2

T₁ = 15053.79 N-mm

T₂ = 34946.21 N-mm

Part b

Angle of rotation = (T₁L₁/G₁J₁)

(15053.79*500) / (14000*981.75) = 0.548 radians

Part c

Maximum stress in material 1 =q_1max

R = radius

(T1/J1) = (q_1max/R1)

q_1max = (15053.79*5) / (981.75) = 76.67 N/mm²

q_2max = (34946.21*7.5) / (3988.35) = 65.72 N/mm²