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For all the questions given below: Solve for the support reactions and construct shear force (V) and bending moment (M) diagrams. Each question is 20 pts.
Please print out this document and solve each question in the designated area. 1. The unit load (w) is 200lb/ft and the concentrated load is 1,500 lb.

To solve this problem, we will start by finding the reactions at the supports for the beam under the given loads. The beam is subjected to a distributed load of \( w = 200 \, \text{lb/ft} \) over a length of 6 ft, and a concentrated load of \( 1500 \, \text{lb} \) located 2 ft from the middle support.

### Step 1: Determine the Reactions at the Supports

Let's define the following points:
- \( A \): the left end of the beam
- \( B \): the point at the roller support (6 ft from \( A \))
- \( C \): the location of the concentrated load (2 ft to the right of \( B \))
- \( D \): the right end of the beam (10 ft from \( C \))

#### Equilibrium Equations

To find the support reactions, we use the equilibrium conditions:
1. Sum of vertical forces (\( \Sigma F_y = 0 \))
2. Sum of moments about any point (\( \Sigma M = 0 \))

Define the reactions at the supports:
- \( R_B \): the reaction at the roller support at point B
- \( R_D \): the reaction at the pin support at point D

#### Calculating the Distributed Load

The total distributed load over the 6 ft length is:
\[
w \times \text{length} = 200 \, \text{lb/ft} \times 6 \, \text{ft} = 1200 \, \text{lb}
\]

This load acts at the centroid of the distributed load, which is 3 ft from point \( A \) or 3 ft to the left of point \( B \).

#### Moment About Point D

Taking moments about point \( D \):
\[
\Sigma M_D = 0 = R_B \times 10 - 1200 \times 13 + 1500 \times 8
\]

Solving for \( R_B \):
\[
10R_B = 15600 - 9600 \\
10R_B = 6000
R_B = 600 lb
\]

Solving for RD 
\[
R = load_1 - R 
= support reacts \]




For the beam problem: Solve for the support reactions and construct shear force (V) and bending moment (M) diagrams. The beam has a distributed load w=200 lb/ft over 6 ft and a concentrated load of 1,500 lb at 2 ft from the middle support.

Learn how to solve a beam problem with a distributed load of 200 lb/ft and a concentrated load of 1,500 lb. This includes calculating the support reactions and constructing shear force and bending moment diagrams. Suitable for engineering students.

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