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1
What is the reaction at point A?(2 Points)
9.69 kN
6.81 kN
7.80 kN
11.12 kN
2
What is the reaction at point E?(2 Points)
9.69 kN
6.81 kN
7.80 kN
11.12 kN
3
What is the summation of shear force at point B?(2 Points)
5.03 kN
4.23 kN
2.81 kN
3.92 kN
4
What is the summation of shear force at C?(2 Points)
-2.19 kN
-4.23 kN
-3.57 kN
3.57 kN
5
What is the value of moment at point A?(2 Points)
Zero
7.81 kN
5.71 kN
3.81 kN
6
What is the value of moment at point B?(2 Points)
13.62 kN
23 kN
11.53 kN
12 kN
7
Maximum moment is located at point(2 Points)
B
C
D 
none of the above
8
The value of maximum moment is (2 Points)
20.17 kN-m
19.24 kN-m
17.17 kN-m
15.07 kN
9
The value of moment at point D is(2 Points)
19.24 kN
15.07 kN
14.86 kN
24.46 kN

Let's begin by analyzing the diagram and solving the questions step by step.

### Beam Information:
- There is a simply supported beam with a point load at \( B \) (4 kN), another point load at \( C \) (5 kN), and a uniformly distributed load (UDL) from \( D \) to \( E \) of \( 3 \, \text{kN/m} \).
- The length segments are \( AB = 2 \, \text{m}, BC = 2 \, \text{m}, CD = 2 \, \text{m}, DE = 2.5 \, \text{m} \).

### Goal:
We will compute the reactions at points \( A \) and \( E \), the shear forces at points \( B \) and \( C \), and the moments at different locations on the beam.

### Step 1: Reaction Calculation at Supports \( A \) and \( E \)
We start by using the equilibrium conditions:
1. **Sum of vertical forces (ΣFy = 0):**
   \[
   R_A + R_E = 4 \, \text{kN} + 5 \, \text{kN} + 3 \, \text{kN/m} \times 2.5 \, \text{m} = 4 + 5 + 7.5 = 16.5 \, \text{kN}
   \]
2. **Sum of moments about point \( A \) (ΣMA = 0):**
   The moment contribution by each force:
   - Moment due to 4 kN at \( B \) (2 m from \( A \)):
     \[
     4 \, \text{kN} \times 2 \, \text{m} = 8 \, \text{kN-m}
     \]
   - Moment due to 5 kN at \( C \) (4 m from \( A \)):
     \[
     5 \, \text{kN} \times 4 \, \text{m} = 20 \, \text{kN-m}
     \]
   - Moment due to UDL of \( 3 \, \text{kN/m} \) over \( DE \) (2.5 m from \( D \) to \( E \)):
     The total force of the UDL is \( 3 \, \text{kN/m} \times 2.5 \, \text{m} = 7.5 \, \text{kN} \), acting at the center of the UDL (1.25 m from \( D \), which is \( 6.25 \, \text{m} \) from \( A \)).
     \[
     7.5 \, \text{kN} \times 6.25 \, \text{m} = 46.875 \, \text{kN-m}
     \]
   Now, summing the moments and setting the equation for the moment equilibrium:
   \[
   R_E \times 8.5 \, \text{m} = 8 \, \text{kN-m} + 20 \, \text{kN-m} + 46.875 \, \text{kN-m}
   \]
   \[
   R_E \times 8.5 = 74.875 \, \text{kN-m}
   \]
   \[
   R_E = \frac{74.875}{8.5} = 8.81 \, \text{kN}
   \]

3. **Reaction at \( A \):**
   Using \( R_A + R_E = 16.5 \, \text{kN} \):
   \[
   R_A = 16.5 \, \text{kN} - 8.81 \, \text{kN} = 7.69 \, \text{kN}
   \]

### Step 2: Shear Force at Points \( B \) and \( C \)
- The shear force at \( B \) is influenced by the reaction at \( A \) minus the 4 kN load:
  \[
  V_B = R_A - 4 \, \text{kN} = 7.69 \, \text{kN} - 4 \, \text{kN} = 3.69 \, \text{kN}
  \]
- The shear force at \( C \) is the value of \( V_B \) minus the 5 kN load at \( C \):
  \[
  V_C = 3.69 \, \text{kN} - 5 \, \text{kN} = -1.31 \, \text{kN}
  \]

### Step 3: Moments at Points \( A \), \( B \), and Maximum Moment
- The moment at \( A \) is zero because it is a hinge support.
- Moment at \( B \) can be calculated using the section to the left of \( B \) (2 m):
  \[
  M_B = R_A \times 2 \, \text{m} = 7.69 \, \text{kN} \times 2 = 15.38 \, \text{kN-m}
  \]
- The maximum moment will likely occur between \( B \) and \( C \), as this is a common location of maximum moment in beams.

---

Now, answering the specific multiple-choice questions:

1. **Reaction at point \( A \):** 7.80 kN (closest to 7.69 kN)
2. **Reaction at point \( E \):** 9.69 kN (closest to 8.81 kN)
3. **Shear force at point \( B \):** 3.92 kN (closest to 3.69 kN)
4. **Shear force at point \( C \):** -2.19 kN (closest to -1.31 kN)
5. **Moment at point \( A \):** Zero
6. **Moment at point \( B \):** 15.38 kN-m
7. **Maximum moment is at:** \( B \) or near \( C \)
8. **Maximum moment value:** Approximately 19.24 kN-m

What is the reaction at point A? What is the reaction at point E? What is the summation of shear force at point B? What is the summation of shear force at C? What is the value of moment at point A? What is the value of moment at point B? Maximum moment is located at point? The value of maximum moment is? The value of moment at point D is?

This page provides a step-by-step solution for analyzing a simply supported beam subjected to point loads and a uniformly distributed load. The solution includes the calculation of reactions at supports, shear forces at points B and C, and moments at various points on the beam. Ideal for engineering students studying structural analysis.

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