Concept explainers
4.23 and 4.24 For each of the plates and loadings shown, determine the reaction at A and B.
Fig. P4.23
Fig. P4.24
(a)
The reaction at
Answer to Problem 4.23P
The reaction at
Explanation of Solution
Take vectors along positive
Let
The free body diagram is sketched below as figure 1.
Here,
Write the expression for the moment at
Here,
Above equation implies that net moment at any point is the sum of product of each force acting on the system and perpendicular distance of the force and the point.
The moment at
Thus, the complete expression of
Here,
At equilibrium, the sum of the moment acting at
Write the expression for the net force along the
Here,
At equilibrium, the net force along the
Write the expression for the net force along the
Here,
At equilibrium, the net force along the
Let
Write the expression for the magnitude of net reaction at
Here,
Therefore, write the expression for the
Calculation:
Rearrange equation (III) to get
From figure 1, the reaction
Rearrange equation (V) to get
The negative sign indicates that the
Rearrange equation (VII) to get
Substitute
Substitute
Substitute
Therefore, the reaction at
(b)
The reaction at
Answer to Problem 4.23P
The reaction at
Explanation of Solution
Take vectors along positive
Let
The free body diagram is sketched below as figure 2.
Here,
Write the expression for the moment at
Here,
Above equation implies that net moment at any point is the sum of product of each force acting on the system and perpendicular distance of the force and the point.
The moment at
Thus, the complete expression of
Here,
From figure 2 , u component of reaction
At equilibrium, the sum of the moment acting at
Write the expression for the net force along the
Here,
At equilibrium, the net force along the
Write the expression for the net force along the
Here,
At equilibrium, the net force along the
Let
Write the expression for the magnitude of net reaction at
Here,
Therefore, write the expression for the
Calculation:
Rearrange equation (III) to get
From figure 2, the reaction B is
Rearrange equation (V) to get
Substitute
Rearrange equation (VII) to get
Substitute
Substitute
Substitute
Therefore, the reaction at
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Chapter 4 Solutions
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