The members of the truss are all of length L. Determine the axial forces in the members and indicate whether they are in tension (T) or compression (C).
Solution
Force balance at point A:
x-dir: EQ1
- F_f*sin(theta) - Fab*d/sqrt(d^2+h^2) + Fac*d/sqrt(d^2+h^2) = 0
y-dir: EQ2
-F_f*cos(theta) - Fab*h/sqrt(d^2+h^2) - Fac*h/sqrt(d^2+h^2) = 0
Solve EQ1 and EQ2 for Fab and Fac
Results:
Fab = -1/2*(d^2+h^2)^(1/2)/d/h*F_f*(cos(theta)...
Fac = -1/2*(d^2+h^2)^(1/2)*F_f*(-h*sin(theta)+...
Force balance at point B will give zero results, because there are two reactions:
Force balance at point C:
x-direction:
- Fac*d/sqrt(d^2+h^2) - Fbc = 0
Solve for Fbc:
Fbc = -Fac*d/sqrt(d^2+h^2)
Substitute:
Fbc = 1/2*F_f*(cos(theta)*d - h*sin(theta))/h
y-direction is unnecessary, because we don\'t care about the support reaction.
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Organic Name Reactions for the students and aspirants of Chemistry12th.pptx
The members of the truss are all of length L- Determine the axial forc.docx
1. The members of the truss are all of length L. Determine the axial forces in the members and
indicate whether they are in tension (T) or compression (C).
Solution
Force balance at point A:
x-dir: EQ1
- F_f*sin(theta) - Fab*d/sqrt(d^2+h^2) + Fac*d/sqrt(d^2+h^2) = 0
y-dir: EQ2
-F_f*cos(theta) - Fab*h/sqrt(d^2+h^2) - Fac*h/sqrt(d^2+h^2) = 0
Solve EQ1 and EQ2 for Fab and Fac
Results:
Fab = -1/2*(d^2+h^2)^(1/2)/d/h*F_f*(cos(theta)...
Fac = -1/2*(d^2+h^2)^(1/2)*F_f*(-h*sin(theta)+...
Force balance at point B will give zero results, because there are two reactions:
Force balance at point C:
x-direction:
- Fac*d/sqrt(d^2+h^2) - Fbc = 0
Solve for Fbc:
Fbc = -Fac*d/sqrt(d^2+h^2)
Substitute:
Fbc = 1/2*F_f*(cos(theta)*d - h*sin(theta))/h
y-direction is unnecessary, because we don't care about the support reaction.
