# ## Problems: Chapter 7

1- Find the shear forces and bending moments at the sections shown. For the bending moment at S3 consider sections right before and after S3.

Section 1 at : .

Section 2 at : .

Section 3 at : .

2- Find the shear forces and bending moments at the sections shown.

Section 1 at : .

Section 2 at : .

3- Find the shear forces and bending moments at the sections shown.

Section 1 at : .

Section 2 at : .

Section 3 at : .

4- Find the shear forces and bending moments at the sections shown.

Section 1 at : .

Section 2 at : .

5- Determines the functions and .  6- Determines the functions and . Consider the support at as a roller in a slot if the support reaction becomes a pulling force there. 7- Determine the functions and .  8- For the loaded beam shown, find the locations where the shear force and the bending moment attain their maximum magnitudes. Then, determine the maximum magnitudes. Hint: find the local and global extrema (maxima or minima) of the functions and . Use derivatives for finding local extrema. You can also plot and for more clarification.

The maximum magnitude of the shear force is and it occurs at two locations being the supports, i.e. and .

The maximum magnitude of the bending moment is occurring at .

9- For the loaded beam shown, find the locations where the shear force and the bending moment attain their maximum magnitudes. Then, determine the maximum magnitudes. Hint: see the previous problem.

The maximum magnitude of the shear force is occurring at , i.e. support .

The maximum magnitude of the bending moment is occurring at .

10- For the loaded beam shown, find the locations where the shear force and the bending moment attain their maximum magnitudes. Then, determine the maximum magnitudes. Hint: see the previous problem.

The maximum magnitude of the shear force is occurring at and i.e. the supports.
The maximum magnitude of the bending moment is occurring at .
The maximum magnitude of the shear force is occurring at i.e. the support.
The maximum magnitude of the bending moment is occurring at i.e. the support.