Recent interest in competitive and recreational cycling has meant that engineers have dire...

Recent interest in competitive and recreational cycling has meant that engineers have directed their skills toward the design and testing of mountain bikes (Fig. P7.15a). Suppose that you are given the task of predicting the horizontal and vertical displacement of a bike bracketing system in response to a force. Assume the forces you must analyze can be simplified as depicted in Fig. P7.15b. You are interested in testing the response of the truss to a force exerted in any number of directions designated by the angle θ. The parameters for the problem are E = Young’s modulus = 2 × 10¹¹ Pa, A = cross-sectional area = 0.0001 m², w = width = 0.44 m, ℓ = length = 0.56 m, and h = height = 0.5 m. The displacements x and y can be solved by determining the values that yield a minimum potential energy. Determine the displacements for a force of 10,000 N and a range of θ’s from 0° (horizontal) to 90° (vertical).

FIGURE P7.15: (a) A mountain bike along with (b) a free-body diagram for a part of the frame.