Question

A circular cross section, d = 25 mm, experiences a torque load, T = 25 N·m, and a shear force, V = 85 kN. Calculate the largest shear stress within the cross section. B. 239 MPa A. 231 MPa C. 8.15 MPa D. 95.6 MPa

Answer 1

largest shear stress = 239 N/mm²

Step-by-step explanation:

Given data

cross section d = 25 mm

torque load T = 25 N·m

shear force V = 85 kN

to find out

largest shear stress

solution

we know that maximum shear stress due to load = 16T / πd³

maximum shear stress = 16 ( 25)
`10^(3)` / π(25)³

maximum shear stress = 8.148 N/mm² ........................1

maximum shear stress due to force = 14/3 × avg shear stress

maximum shear stress due to force = 14 × 85 ×
`10^(3)` / (3 ×π/4×25²)

maximum shear stress due to force = 230.88 N/mm² ..................2

so

largest shear stress add equation 1 and 2

largest shear stress = 8.148 + 230.88

largest shear stress = 239 N/mm²