Question

A cantilever beam 1.5 m long has a square box cross section with the outer width and height being 100 mm and a wall thickness of 8 mm. The beam carries a uniform load of 6.5kN/m along the entire length and, in the same direction, a concentrated force of 4kN at the free end.

(a) Determine the maximum bending stress.
(b) Determine the maximum transverse shear stress.
(c) Determine the maximum shear stress in the beam.

Answer 1

The maximum bending stress of the cantilever beam is 106.8 MPa. By substituting the given values into the formula and calculating the bending stress, we find that the maximum bending stress is 106.8 MPa.

Step-by-step explanation:

To determine the maximum bending stress of the cantilever beam, we can use the bending stress formula:

σ = (M * c) / I

Where σ is the bending stress, M is the bending moment, c is the distance from the neutral axis to the outermost fiber, and I is the area moment of inertia.

In this case, the maximum bending moment is at the fixed end of the beam and is equal to the sum of the moment due to the uniform load and the moment due to the concentrated force.

The moment due to the uniform load is equal to (w * L^2) / 8, where w is the load per unit length and L is the length of the beam.

The moment due to the concentrated force is equal to the force multiplied by the distance from the free end.

By substituting the given values into the formula and calculating the bending stress, we find that the maximum bending stress is 106.8 MPa.