Classify each of the following trusses as statically determinate, statically indeterminate, or unstable. If indeterminate, state its degree.
(a)
If, the truss is statically determinate, statically indeterminate or unstable and its degree.
Answer to Problem 3.1P
The truss is statically determinate.
Explanation of Solution
Given:
One end of the truss has roller support and the other end has pinned support.
Concept Used:
The determinacy of the structure is obtained from the formula:
If
If
If
Where j is the number of joints.
m is the number of members of the truss.
r is the number of reactions at the support.
In case of pinned support there are two reactions.
In case of roller support there is only one reaction.
In case of fixed support there are three reactions.
In case of simple support there is only one reaction.
Calculation:
Here,
Which implies that the truss is statically determinate.
Conclusion:
Hence, the truss is statically determinate.
(b)
If, the truss is statically determinate, statically indeterminate or unstable and its degree if indeterminate.
Answer to Problem 3.1P
The truss is statically indeterminate.
Degree of indeterminacy i=2.
Explanation of Solution
Given:
Both the ends of the truss have pinned joint.
Concept Used:
The determinacy of the structure is obtained from the formula:
If
If
If
Where j is the number of joints.
m is the number of members of the truss.
r is the number of reactions at the support.
In case of pinned support there are two reactions.
In case of roller support there is only one reaction.
In case of fixed support there are three reactions.
In case of simple support there is only one reaction.
Calculation:
Here,
Which implies that the truss is statically indeterminate with degree of indeterminacy as 2.
Conclusion:
Truss is statically indeterminate.
Degree of indeterminacy i=2.
(c)
If, the truss is statically determinate, statically indeterminate or unstable. If statically indeterminate and its degree.
Answer to Problem 3.1P
The truss is statically determinate.
Explanation of Solution
Given:
One end of the truss has pinned support and the other end has roller support.
Concept Used:
The determinacy of the structure is obtained from the formula:
If
If
If
Where j is the number of joints
m is the number of members of the truss
r is the number of reactions at the support
In case of pinned support there are two reactions
In case of roller support there is only one reaction
In case of fixed support there are three reactions
In case of simple support there is only one reaction
Calculation:
Here,
Which implies that the truss is statically determinate.
Conclusion:
Truss is statically determinate.
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