## Problems: Chapter 7

1- Find the shear forces and bending moments at the sections shown. For the bending moment at S_{3} consider sections right before and after S_{3}.

**Answer**

Section 1 at : .

Section 2 at : .

Section 3 at : .

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

**Answer**

Section 1 at : .

Section 2 at : .

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

**Answer**

Section 1 at : .

Section 2 at : .

Section 3 at : .

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

**Answer**

Section 1 at : .

Section 2 at : .

5- Determines the functions and .

**Answer**

6- Determines the functions and . Consider the support at as a roller in a slot if the support reaction becomes a pulling force there.

**Answer**

7- Determine the functions and .

**Answer**

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.

**Answer**

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.

**Answer**

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.

**Answer**

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 .

11- 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.

**Answer**

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.