Question

Determine the axial forces, shears, and bending moments at points A and B of the structure shown.

Answer 1

Draw free body diagram of the inclined beam.

Calculate Inclination of the beam.

Apply equilibrium conditions to calculate the support reactions.

Consider forces along X-direction.

Consider moment about the point D,

Consider forces along Y-direction.

The forces acting on the beam are oriented along the axis of the beam and normal to the beam as shown in the figure:

The uniformly distributed load acting on the beam is divided into two components.

Calculate when the uniformly distributed load acting along the axis of the beam,

Calculate when the uniformly distributed load acting normal to the axis of the beam,

Calculate the normal reaction at point C, along the axis of the beam,

Calculate the normal reaction at point C, along the normal to the axis of the beam,

Calculate the normal reaction at point D, along the axis of the beam,

Calculate the normal reaction at point D, along the normal to the axis of the beam,

Draw free body diagram of the member CA with axial force, shear force and bending moment.

Calculate the axial force at point A.

Consider forces along the axial direction.

Therefore, the axial force at point A is .

Calculate the shear force at point A.

Consider forces along vertical direction.

Therefore, the shear force at point A is .

Calculate the bending moment at point A.

Consider moment about .

Therefore, bending moment at point A, .

Draw free body diagram of the member BD with axial force, shear force and bending moment.

Calculate the axial force at point B.

Consider forces along the axial direction.

Therefore, the axial force at point B is .

Calculate the shear force at point B.

Consider forces along vertical direction.

Therefore, the shear force at point B is .

Calculate the bending moment at point B.

Therefore, bending moment at point B is .