Explanation Sign conversion: Apply the sign convention for calculating the equations of equilibrium as below. For the horizontal forces equilibrium condition, take the force acting towards right side as positive ( → + ) and the force acting towards left side as negative ( ← − ) . For the vertical forces equilibrium condition, take the upward force as positive ( ↑ + ) and downward force as negative ( ↓ − ) . For moment equilibrium condition, take the clockwise moment as negative and counter clockwise moment as positive. Apply the following sign convention for calculating the axial forces, shear and bending moments. When the portion of the beam considered is left of the section, then the external force acting to the left are considered as positive. When the portion of the beam considered is right of the section, then the external force acting to the right are considered as positive. When the portion of the beam considered is left of the section, then the external force acting upward are considered as positive. When the portion of the beam considered is right of the section, then the external force acting downward are considered as positive. When the portion of the beam considered is left of the section, then the clockwise moments are considered as positive. When the portion of the beam considered is right of the section, then the counterclockwise moments are considered as positive. Calculation: Show the free-body diagram of the section from hinge to right end E as in Figure 1. Refer Figure 1, Find the vertical reaction at point E by taking moment about the hinge. + ↺ ∑ M hinge = 0 ( − 20 × 10 × 10 2 ) + E y ( 10 ) = 0 − 1 , 000 + 10 E y = 0 E y = 100 kN ( ↑ ) Show the free-body diagram of the entire beam as in Figure 2. Find the horizontal reaction at point C by resolving the horizontal equilibrium. + → ∑ F x = 0 C x = 0 Find the moment at point C by taking moment about the point D . + ↺ ∑ M D = 0 C y × 10 + 20 × 10 × 10 2 − 20 × 20 × 20 2 + 100 ( 20 ) = 0 10 C y = 1 , 000 C y = 100 kN ( ↓ ) Find the vertical reaction at point C by resolving the vertical equilibrium. + ↑ ∑ F y = 0 − 100 − 20 × 30 + D y + 100 = 0 D y = 600 kN ( ↑ ) Pass the sections aa and bb at points A and B respectively. Show the sections aa and bb as in Figure 3. Consider section aa : Consider the left side of the section aa for calculation of internal forces. Show the free-body diagram of the left side of the section aa as in Figure 4

5th Edition

ISBN: 9780100469105

Author: KASSIMALI

Publisher: YUZU

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Question

Chapter 5, Problem 9P

To determine

Find the axial force, shear, and bending moment at points A and B of the beam.

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Chapter 5, Problem 8P

Chapter 5, Problem 10P

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