Concept explainers
A soccer goal is subjected to gravity loads (in the - z direction, w = 73 N/m for DG, BG, and BC; w = 29 N/m for all other members; see figure) and a force F = 200 N applied eccentrically at the mid-height of member DG. Find reactions at sup ports C, D, and H.
The reactions at support
The reaction at support
The reaction at support
Answer to Problem 1.3.32P
The reactions at support
The reactions at support
The reactions at support
Explanation of Solution
The weight per unit length in the members
The following figure shows the forces on the goal post.
Figure-(1)
Write the expression for the length of the members
Here, the length of member
Write the expression for horizontal component of force on member
Here the horizontal component of force is
Write the expression for the vertical component of force on member
Here, the vertical component of force is
Write the expression for moment about x axis.
Here, the force along the member
Write the expression for moment about Y axis.
Here, the length of member
Write the expression for moment about Z axis and equate it to zero.
Here, the reaction of Y axis about
Write the expression for the sum of forces about x axis.
Write the expression for the sum of forces about Y axis.
Write the expression for the sum of forces about Z axis.
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
The following figure shows the free body diagram of forces along y and z axes.
Figure-(2)
Substitute
Substitute
Substitute
Substitute
Conclusion:
The reactions at support
The reactions at support
The reactions at support
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Chapter 1 Solutions
Mechanics of Materials, SI Edition
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