
(a)
Calculate the stiffness co-efficient K.
(a)

Answer to Problem 1P
The stiffness co-efficient K is
Explanation of Solution
Given information:
The modulus of elasticity (E) is 30,000 ksi.
The vertical displacement of joint A
The vertical load acting at joint A is 24 kips.
Calculation:
Show the free body diagram of the structure as in Figure (1).
Refer Figure (1),
Find the force in the member AC using the relation;
Find the angle in the member;
Find the inclined displacement of joint A;
Find the force in the member AB using the relation;
Find vertical force in the member AB;
Find horizontal force in the member AB;
Show the free body diagram of the joint A as in Figure (2).
Refer Figure (2),
Consider the upward force is positive and downward force is negative.
Find the stiffness coefficient;
Summation of forces along y-direction is equal to 0.
Thus, the stiffness co-efficient K is
(b)
Calculate the vertical displacement at A.
(b)

Answer to Problem 1P
The vertical displacement at A is
Explanation of Solution
Find the vertical displacement at A;
Thus, the vertical displacement at A is
(c)
Calculate the axial forces in all bars.
(c)

Answer to Problem 1P
The axial force in the member AC is
The axial force in the member AB and AD is
Explanation of Solution
Find the axial force in the member AC using the relation;
Thus, the axial force in the member AC is
Find the force in the member AB and AD using the relation;
Thus, the axial force in the member AB and AD is
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Chapter 14 Solutions
Fundamentals of Structural Analysis
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