Pipe (2) is supported by a pin at bracket C and by tie rod (1). The structure supports a load P at pin B. Tie rod (1) has a diameter of 12 mm and an allowable normal stress of 110 MPa. Pipe (2) has an outside diameter of 48 mm, a wall thickness of 5 mm, and an allowable normal stress of 65 MPa. Assume x1Determine the maximum load Pmax that can be supported by the structure without exceeding either allowable normal stress.

P_max = 25204 N

Explanation:

Given:

- Rod 1 : Diameter D = 12 mm, stress_1 = 110 MPa

- Rod 2: OD = 48 mm, thickness t = 5 mm, stress_2 = 65 MPa

- x_1 = 3.5 mm; x_2 = 2.1 m; y_1 = 3.7 m

Find:

- Maximum Force P_max that this structure can support.

Solution:

- We will investigate the maximum load that each Rod can bear by computing the normal stress due to applied force and the geometry of the structure.

- The two components of force P normal to rods are:

Rod 1 : P*cos (Q)

Rod 2: - P*sin (Q)

where Q: angle subtended between x_1 and Rod 1 @ A. Hence,

Q = arctan (y_1 / x_1)

Q = arctan (3.7 / 2.1) = 60.422 degrees.

- The normal stress in each Rod due to normal force P are:

Rod 1 : stress_1 = P*cos (Q) / A_1

Rod 2: stress_2 = - P*sin (Q) / A_2

- The cross sectional Area of both rods are A_1 and A_2:

A_1 = pi*D^2 / 4

A_2 = pi * (OD^2 - ID^2) / 4

- The maximum force for the given allowable stresses are:

Rod 1: P_max = stress_1 * A_1 / cos (Q)

P_max = (110*10^6) * pi*0.012^2 / 4*cos (60.422)

P_max = 25203.61848 N

Rod 2: P_max = stress_2 * A_2 / sin (Q)

P_max = (65*10^6) * pi * (0.048^2 - 0.038^2) / 4*sin (60.422)

P_max = 50483.4 N

- The maximum force that the structure can with-stand is governed by the member of the structure that fails first. In our case Rod 1 with P_max = 25204 N.