A pin-connected truss composed of members AB and BC is subjected to a vertical f

Question

A pin-connected truss composed of members AB and BC is subjected to a vertical force of 40 kN at joint B. The constant cross-sectional areas of members AB and BC are 0.004 m2 and 0.002 m2 respectively. The diameter of the pin is 20 mm, clevis thickness is 10 mm, and bracket thickness is 15 mm. Determine the forces in the members AB and BC of the truss in terms of kN the normal stresses acting in the members AB and BC of the truss in terms of MPa, the shearing stress in the pin in terms of MPa and the bearing stresses in the bracket and clevis at joint C in terms of MPa.

Explanation / Answer

let F1(x1,y1) be the force acting at point (x,y)

let F2(x2,y2) be the force acting at point (x,y)

and let F3(x3,y3) be the force acting at point (x,y)

the resultant of the three forces is

F = (Fx^2 + Fy^2)^1/2

where Fx = F1 x cosA + F2 x cosB + F3 x cosC

and Fy = F1 x sinA + F2 x sinB + F3 x sinC

where A,B and C are angles given by

A = tan^-1(y1 - y/x1 - x),

B = tan^-1(y2 - y/x2 - x) and

C = tan^-1(y3 - y/x3 - x)

the angle made by the resultant force is

X = tan^-1(Fy/Fx)

the angle X is counter clockwise from the positive x axis

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