Answer:
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.
