Questions: Resolver par Nodos.

Resolver par Nodos.
Transcript text: Resolver par Nodos.
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Solution

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Solution Steps

Step 1: Identify the Support Reactions
  • Identify the types of supports at points A and E.
  • Point A has a pin support, which can exert both horizontal (Ax) and vertical (Ay) reactions.
  • Point E has a roller support, which can exert only a vertical reaction (Ey).
Step 2: Apply Equilibrium Equations
  • Use the equilibrium equations to solve for the support reactions.
  • Sum of forces in the horizontal direction (ΣFx = 0): \[ Ax + 30\cos(38.86^\circ) - 40\cos(53.13^\circ) = 0 \]
  • Sum of forces in the vertical direction (ΣFy = 0): \[ Ay + Ey - 25 - 30\sin(38.86^\circ) - 40\sin(53.13^\circ) = 0 \]
  • Sum of moments about point A (ΣMA = 0): \[ 25 \times 6 + 40 \times 6 \cos(53.13^\circ) - Ey \times 12 = 0 \]
Step 3: Solve for Support Reactions
  • Solve the moment equation for Ey: \[ Ey = \frac{25 \times 6 + 40 \times 6 \cos(53.13^\circ)}{12} \]
  • Substitute Ey back into the vertical force equilibrium equation to solve for Ay: \[ Ay = 25 + 30\sin(38.86^\circ) + 40\sin(53.13^\circ) - Ey \]
  • Substitute Ay into the horizontal force equilibrium equation to solve for Ax: \[ Ax = -30\cos(38.86^\circ) + 40\cos(53.13^\circ) \]

Final Answer

  • The support reactions are: \[ Ax = -30\cos(38.86^\circ) + 40\cos(53.13^\circ) \] \[ Ay = 25 + 30\sin(38.86^\circ) + 40\sin(53.13^\circ) - Ey \] \[ Ey = \frac{25 \times 6 + 40 \times 6 \cos(53.13^\circ)}{12} \]
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