Explanation Given information: The beam is made of polyester that has the stress-strain curve. The portion of the curve is represented by an equation σ = [ 20 tan − 1 ( 15 ∈ ) ] ksi , where tan − 1 ( 15 ∈ ) is in radians. Determine the reactions: Show the free body diagram of the entire beam as in Figure 1. Moment about point B : Determine the vertical reaction at point A by taking moment about point B . ∑ M B = 0 P × 8 − A y ( 16 ) = 0 A y = P 2 Along the vertical direction: Determine the vertical reaction at point B by resolving the vertical component of forces. ∑ F y = 0 A y + B y − P = 0 (1) Substitute P 2 for A y in Equation (1). P 2 + B y − P = 0 B y = P 2 Along the horizontal direction: Determine the horizontal reaction at point B by resolving the horizontal component of forces. ∑ F x = 0 B x = 0 Maximum bending moment: Moment at x = 0 : M | x = 0 = 0 Moment at x = 8 ft : M | x = 8 ft = A y ( 8 ) = P 2 ( 8 ) = 4 P Moment at x = 16 ft : M | x = 16 ft = A y ( 16 ) − P ( 8 ) = P 2 ( 16 ) − P ( 8 ) = 0 The maximum bending moment will occur at mid-point. Show the bending moment diagram of the beam as in Figure 2. Maximum bending moment: The maximum bending moment in the beam is as follows: M max = 4 P (2) Strain distribution: Show the strain distribution in the beam as in Figure 3. Refer to Figure 3: The strain corresponding to y distance from neutral axis is as follows: 0.003 2 = ∈ y ∈ = 0.0015 y Stress distribution: Show the stress distribution in the beam as in Figure 4. The relationship between stress and strain is given by the equation. σ = [ 20 tan − 1 ( 15 ∈ ) ] ksi (3) Substitute 0.0015 y for ∈ in Equation (3). σ = [ 20 tan − 1 ( 15 × 0

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Axial Load

When a bar of the uniform cross-section is acted by a load, such that the load acts along the longitudinal axis of the bar, such kinds of loadings are known as axial loadings. In general terms, a load is an external force acting on a component. An axial …

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Chapter 6.10, Problem 6.177P

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The magnitude of the force P that can be applied to the beam without causing the maximum strain in its fibres at the critical section to exceed εmax=0.003 in./in. .

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Chapter 6.10, Problem 6.176P

Chapter 6.10, Problem 6.178P

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The magnitude of the force P that can be applied to the beam without causing the maximum strain in its fibres at the critical section to exceed ε max = 0.003 in ./in . .

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The magnitude of the force P that can be applied to the beam without causing the maximum strain in its fibres at the critical section to exceed εmax=0.003 in./in. .

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