Shear and Bending Moment Diagrams - Exercises

For the following beams:
- Find the reactions
- Draw the shear diagram
- Draw the moment diagram

Beam 1: (P = 20 KN - L = 3.9 metres - a = 1.8 metres)
For the given cross section of the beam:
- find the maximum bending stress
- find the maximum shearing stress

Beam 2:

For the given cross section of the beam, the maximum allowable bending stress is ?? = 180 ?????? Find the minimum required depth ‘d' for a safe design. What is the maximum shear stress for this ‘d' value and where in the beam does it occur?

Beam 3: (w = 4 KN/m - L = 3.2 metres - a = 1.3 metres)

For the given cross section of the beam, the maximum allowable bending stress is ?? = 180 ?????? Find the minimum required width ‘w' for a safe design. What is the maximum shear stress for this ‘w' value and where in the beam does it occur?

Beam 4: (w = 5 KN/m - a = 1.8 metres - b = 2.2 metres)

For the given cross section of the beam, find the maximum bending stress at mid-span.

Draw a shear stress profile at support A and at midspan.

Beam 5: (w = 4.5 KN/m - a = 1.6 metres - L = 6.7 metres)

For the given cross section of the beam, find the magnitude of the maximum bending stress at support B.

Calculate the maximum shear stress in the beam and draw a shear stress profile/diagram for cross-section where the maximum shear stress occurs.

Beam 6: (Note the hinge at B and the fixed support at C)

For the given cross section of the beam, find the magnitude of the bending stress 2.5 metres to the right of support A.

At that same location draw the shear stress profile/diagram of the cross-section.

Beam 7:

For the given cross section of the beam, find the magnitude of the maximum bending stress 2 metres to the left of support B.

At that same location draw the shear stress profile/diagram of the cross-section.

Beam 8: (P = 22 KN - L = 1.6 metres)

What dimensions of a rectangular cross section with a shape ratio of ½ are adequate if the maximum allowable bending stress in the beam is 120 MPa? Provided the maximum allowable shearing stress in the beam is limited to 30 MPa, are the selected dimensions selected using the criterion for bending stress adequate? If not, what should the dimensions of the beam be?

Beam 9: (P = 26 KN - L = 2.0 metres)

For the given cross section of the beam, find the magnitude of the maximum compressive bending stress and also the magnitude of the maximum tensile bending stress.

What is the maximum shear stress in the beam and where in the beam does it occur?