The structure stiffness matrix for the truss.
Answer to Problem 14.1P
The structure stiffness matrix for the truss is shown below.
Explanation of Solution
Concept Used:
Write the expression for direction cosine in x-direction.
Here, coordinate of
Write the expression for direction cosine in x-direction.
Here, coordinate of
Write the stiffness matrix for the member.
Here, cross-sectional area of the member is
Write the expression for total structural stiffness matrix.
Here, the structural stiffness matrix is
Calculation:
The free body diagram of the truss is shown below.
Figure (1)
Consider the member-1.
Calculate the length of member
Calculate direction cosine in x-direction.
Substitute
Calculate direction cosine in y-direction.
Substitute
The stiffness matrix for member-1 is shown below.
Substitute
Consider the member-
Calculate the length of member
Calculate direction cosine in x-direction.
Substitute
Calculate direction cosine in y-direction.
Substitute
The stiffness matrix for member-2 is shown below.
Substitute
Consider the member-
Calculate direction cosine in x-direction.
Substitute
Calculate direction cosine in y-direction.
Substitute
The stiffness matrix for member-3 is shown below.
Substitute
Consider the member-
Calculate the length of member
Calculate direction cosine in x-direction.
Substitute
Calculate direction cosine in y-direction.
Substitute
The stiffness matrix for member-4 is shown below.
Substitute
Consider the member-
Calculate direction cosine in x-direction.
Substitute
Calculate direction cosine in y-direction.
Substitute
The stiffness matrix for member-5 is shown below.
Substitute
Calculate total structural stiffness matrix.
Substitute the values of
Conclusion:
The structure stiffness matrix for the truss is shown below.
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Chapter 14 Solutions
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