Concept explainers
The plane truss in the figure is assembled From steel C 10 X 20 shapes (see Table 3(a) in Appendix F). Assume that L = 10 ft and b = 0 71 L.
(a) If load variable P = 49 kips, what is the maximum shear stress Tmaxin each truss member?
(b) What is the maximum permissible value of load variable P if the allowable normal stress is 14 ksi and the allowable shear stress is 7.5 ksi?
(a)
The maximum shear stress in the member AC.
The maximum shear stress in the member AB.
The maximum shear stress in the member BC.
Answer to Problem 2.6.11P
The maximum shear stress in the member AC is =
The maximum shear stress in the member AB is =
The maximum shear stress in the member BC is =
Explanation of Solution
The following figure shows the forces on the truss:
Figure-(1)
Write the expression for the length
Write the expression for the length CD.
Here, the length of
Write the expression for the length AD.
Write the expression for the angle
Here, the length of the member CB is
Write the expression for the length DB.
Write the expression for the length AB.
Write the expression for the moment at point A.
Here, the variable load is
Write the equilibrium equation for the horizontal forces.
Write the equilibrium equation for the vertical forces.
Write the expression for the forces at joint A.
Write the expression for the horizontal forces at joint A.
Write the expression for the horizontal forces at joint B.
Write the expression for the maximum shear stress in the member AC.
Write the expression for the maximum shear stress in the member AB.
Write the expression for the maximum shear stress in the member BC.
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Refer to table F-3 (a), “Properties of channel sections” to obtain the area of cross-section of
Substitute
Substitute
Substitute
Conclusion:
The maximum shear stress in the member AC is =
The maximum shear stress in the member AB is =
The maximum shear stress in the member BC is =
(b)
The maximum permissible load.
Answer to Problem 2.6.11P
The maximum permissible load is =
Explanation of Solution
Write the expression for the maximum permissible load on member
Here, permissible normal stress is
Write the expression for the maximum permissible load on member
Here, permissible normal stress is
Calculation:
Substitute
Substitute
The lowest value of the maximum permissible load is =
Conclusion:
The maximum permissible load is =
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