Explanation Given information: The flexural rigidity of the shaft is E I . The load act at point C of the beam ( P 1 ) is 15 kN . The load act at mid of the segment AB of the beam ( P 2 ) is 20 kN . The length of the beam ( L ) is 4 m . Calculation: Show the free body diagram of the beam as in Figure 1. Refer to Figure 1. Calculate the support reactions A and B ( A y and B y ) : Calculate the vertical forces by applying the equation of equilibrium: Sum of vertical forces is equal to 0. ∑ F y = 0 A y + B y − 15 − 20 = 0 A y + B y − 35 = 0 A y + B y = 35 (1) Calculate the moment about point A by applying the equation of equilibrium: Sum of moments about point A is equal to 0. ∑ M A = 0 ( B y × 2 ) − ( 20 × 1 ) + ( 15 × 2 ) = 0 2 B y + 10 = 0 2 B y = − 10 B y = − 10 2 B y = − 5 kN B y = 5 kN ↓ Substitute ( − 5 kN ) for B y in Equation (1). A y − 5 = 35 A y = 35 + 5 A y = 40 kN Show the moment area diagram of the beam as in Figure 2

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ISBN: 2810014920922

Author: HIBBELER

Publisher: PEARSON

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Combined Loading

Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial…

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Chapter 12.4, Problem 12.72P

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the distance between the end of the beam and the pointer (tC/A) .

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Chapter 12.4, Problem 12.71P

Chapter 12.4, Problem 12.73P

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the distance between the end of the beam and the pointer ( t C / A ) .

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Chapter 12 Solutions