Explanation Given information: The point load act at a first and second pulley of the shaft is P . The flexural rigidity of the shaft is E I . The length of the shaft is 3 a . Calculation: Show the free body diagram of the moment areaof the shaft as in Figure 1. Refer to Figure 1. Calculate the vertical forces by applying the equation of equilibrium: Sum of vertical forces is equal to 0. ∑ F y = 0 R A + R B − P − P = 0 R A + R B − 2 P = 0 R A + R B = 2 P (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 ( R B × 2 a ) − ( P × a ) − ( P × 3 a ) = 0 2 a R A − P a − 3 P a = 0 2 a R B − 4 P = 0 R B = 4 P a 2 a R B = 2 P Substitute 2 P for R B in Equation (1). R A + 2 P = 2 P R A = 2 P − 2 P R A = 0 Show the free body diagram of the tangent of the shaft as in Figure 2. Refer to Figure 2. Calculate thevertical distance between the tangentat a point B and A ( t B / A ) : t B / A = 1 2 × ( − P a E I ) × a × a 3 = − P a 3 6 E I Calculate the slope at A ( θ A ) using the formula: θ A = | t B / A | 2 a (2) Substitute ( − P a 3 6 E I ) for t B / A in Equation (2). θ A = | − P a 3 6 E I | 2 a = P a 3 12 a E I = P a 2 12 E I Hence, the slope of the shaft at A ( θ A ) is P a 2 12 E I _

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Author: HIBBELER

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Chapter 12.4, Problem 12.56P

To determine

The slope of the shaft at A (θA).

The deflection of the shaft at D (υD).

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Chapter 12.4, Problem 12.55P

Chapter 12.4, Problem 12.57P

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The slope of the shaft at A ( θ A ) . The deflection of the shaft at D ( υ D ) .

Solution Summary: The author calculates the slope of the shaft at A, and the deflection at D, by applying the equation of equilibrium.

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The slope of the shaft at A (θA).

The deflection of the shaft at D (υD).

Want to see the full answer?

Chapter 12 Solutions

The slope of the shaft at A ( θ A ) . The deflection of the shaft at D ( υ D ) .

Solution Summary: The author calculates the slope of the shaft at A, and the deflection at D, by applying the equation of equilibrium.

Videos

The slope of the shaft at A (θA). The deflection of the shaft at D (υD).

Want to see the full answer?

Chapter 12 Solutions

The slope of the shaft at A (θA).

The deflection of the shaft at D (υD).