Explanation Given information: The bracket is fixed connected to its support. EI is constant. Consider bending effect only. Assumptions: Consider that the right side force as positive and left side as negative in horizontal components of forces. Consider that the upward force as positive and downward as negative in vertical components of forces. Consider that the clockwise moment as negative and anticlockwise moment as positive. Virtual-work equation for the beam as follows: 1 ⋅ Δ = ∫ 0 L m M E I d x (1) Here, 1 is external virtual unit load acting on the beam in the direction of Δ , Δ is displacement caused by the real loads on the beam, m is internal virtual moment in the beam, expressed as a function of x and caused by the external virtual unit load, M is internal moment in the beam, expressed as a function of x and caused by the real loads, E is modulus of elasticity of a member, and I is moment of inertia of the cross-sectional area about the neutral axis. Internal moment in the beam ( M ): Region 0 ≤ x < L beam from left end: Show the free body diagram of the beam for the region 0 ≤ x < L as in Figure 1. Moment about the section: Determine the moment at the section by taking moment about the section. ∑ M x 1 = 0 M 1 + P × x 1 = 0 M 1 = − P x 1 Region 0 < x ≤ L column from top end: Show the free body diagram of the beam for the region 0 < x ≤ L as in Figure 2. Moment about the section: Determine the moment at the section by taking moment about the section. ∑ M x 2 = 0 M 2 + P × L = 0 M 2 = − P L Internal virtual moment in the beam ( m ): Apply a vertical unit load at point A and calculate the moments. Region 0 ≤ x < L beam from left end: Show the free body diagram of the beam for the region 0 ≤ x < L as in Figure 3. Moment about the section: Determine the moment at the section by taking moment about the section. ∑ M x 1 = 0 m 1 + 1 ( x 1 ) = 0 m 1 = − x 1 Region 0 < x ≤ L column from top end: Show the free body diagram of the beam for the region 0 < x ≤ L as in Figure 4. Moment about the section: Determine the moment at the section by taking moment about the section

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ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 14.7, Problem 14.114P

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The vertical displacement of point A on the angle bracket due to the concentrated force P.

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Chapter 14.7, Problem 14.113P

Chapter 14.7, Problem 14.115P

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The vertical displacement of point A on the angle bracket due to the concentrated force P .

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The vertical displacement of point A on the angle bracket due to the concentrated force P.

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