Question

Given the cantilevered isostatic beam shown below, determine the support reactions and diagrams of DEC and DMF efforts. A 2.00 m w1 (kN/m) 3.00 m Structures - Fund. Stability and Resistance w3 (kN/m) AB 1.00 m P3 (kN) w2 (kN/m) 4.00 m 2.00 m P1 (kN) P2 (kN) P3 (kN) RA: 0 0 0 00 22 P1 = (7 + 0) kN P2 = (5 + 2) kN P3 = (4 + 2) kN w1 = (3 + 0) kN/m

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Hermann

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75 Answers

1. **Calculate the reaction force at A (vertical force equilibrium):**

\Sigma F_y = 0

R_A - P1 - P2 - P3 - w1 \times 2 = 0

R_A - 7 - 7 - 6 - 6 = 0

R_A = -8 \, \text{kN}

2. **Calculate the reaction moment at A (taking moments about point A):**

\Sigma M_A = 0

- M_A + P1 \times 2 + P2 \times 5 + P3 \times 9 + \frac{w1 \times 2 \times 1}{2} = 0

- M_A + 7 \times 2 + 7 \times 5 + 6 \times 9 + \frac{3 \times 2 \times 1}{2} = 0

- M_A + 14 + 35 + 54 + 3 = 0

- M_A + 106 = 0

M_A = 18.5 \, \text{kN} \cdot \text{m}

Answer:

R_A = -8 \, \text{kN}

M_A = 18.5 \, \text{kN} \cdot \text{m}

2. **Calculate the reaction moment at A (taking moments about point A):**

Answer:

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