Concept explainers
(a)
Categorize the given truss is stable or unstable.
Verify the truss is determinate or indeterminate in case the truss is stable.
Find the degree of indeterminacy in case the given truss is statically indeterminate.
(a)
Answer to Problem 1P
The plane truss is stable.
The plane truss is statically indeterminate.
The plane truss is indeterminate with indeterminacy of 2.
Explanation of Solution
Use the equations to find the stability of the truss.
Here, the b is the number of bars and n is the joints.
Show the conditions for static instability, determinacy, and indeterminacy of the plane truss as follows:
Here, r is the support reactions.
Show the expression for the degree of static indeterminacy (i) as follows:
Refer the Figure of the given plane truss.
The number of the bars in the plane truss is
The number of reaction is
The number of the joints in the plane truss is
Substitute the values of b, r, and n with Equation (2).
Thus, the plane truss is stable.
Substitute the values of b, r, and n with Equation (5).
Thus, the plane truss is statically indeterminate.
Find the degree of static indeterminacy of the truss as follows:
Substitute the values of b, r, and n with Equation (6).
Thus, the plane truss is indeterminate with indeterminacy of 2.
(b)
Categorize the given truss is stable or unstable.
Verify the truss is determinate or indeterminate in case the truss is stable.
Find the degree of indeterminacy in case the given truss is statically indeterminate.
(b)
Answer to Problem 1P
The plane truss is stable.
The plane truss is statically indeterminate.
The plane truss is indeterminate with indeterminacy of 2.
Explanation of Solution
Refer the Figure of the given plane truss.
The number of the bars in the plane truss is
The number of reaction is
The number of the joints in the plane truss is
Substitute the values of b, r, and n with Equation (2).
Thus, the plane truss is stable.
Substitute the values of b, r, and n with Equation (5).
Thus, the plane truss is statically indeterminate.
Find the degree of static indeterminacy of the truss as follows:
Substitute the values of b, r, and n with Equation (6).
Thus, the plane truss is indeterminate with indeterminacy of 2.
(c)
Categorize the given truss is stable or unstable.
Verify the truss is determinate or indeterminate in case the truss is stable.
Find the degree of indeterminacy in case the given truss is statically indeterminate.
(c)
Answer to Problem 1P
The plane truss is geometrically unstable.
Explanation of Solution
Refer the Figure of the given plane truss.
The number of the bars in the plane truss is
The number of reaction is
The number of the joints in the plane truss is
Substitute the values of b, r, and n with Equation (1).
Thus, the plane truss is geometrically unstable.
(d)
Categorize the given truss is stable or unstable.
Verify the truss is determinate or indeterminate in case the truss is stable.
Find the degree of indeterminacy in case the given truss is statically indeterminate.
(d)
Answer to Problem 1P
The plane truss is stable.
The plane truss is statically indeterminate.
The plane truss is indeterminate with indeterminacy of 2.
Explanation of Solution
Refer the Figure of the given plane truss.
The number of the bars in the plane truss is
The number of reaction is
The number of the joints in the plane truss is
Substitute the values of b, r, and n with Equation (2).
Thus, the plane truss is stable.
Substitute the values of b, r, and n with Equation (5).
Thus, the plane truss is statically indeterminate.
Find the degree of static indeterminacy of the truss as follows:
Substitute the values of b, r, and n with Equation (6).
Thus, the plane truss is indeterminate with indeterminacy of 2.
(e)
Categorize the given truss is stable or unstable.
Verify the truss is determinate or indeterminate in case the truss is stable.
Find the degree of indeterminacy in case the given truss is statically indeterminate.
(e)
Answer to Problem 1P
The plane truss is geometrically unstable.
Explanation of Solution
Refer the Figure of the given plane truss.
The number of the bars in the plane truss is
The number of reaction is
The number of the joints in the plane truss is
Substitute the values of b, r, and n with Equation (1).
Thus, the plane truss is geometrically unstable.
(f)
Categorize the given truss is stable or unstable.
Verify the truss is determinate or indeterminate in case the truss is stable.
Find the degree of indeterminacy in case the given truss is statically indeterminate.
(f)
Answer to Problem 1P
The plane truss is stable and determinate.
Explanation of Solution
Refer the Figure of the given plane truss.
The number of the bars in the plane truss is
The number of reaction is
The number of the joints in the plane truss is
Substitute the values of b, r, and n with Equation (4).
Thus, the plane truss is stable and determinate.
(g)
Categorize the given truss is stable or unstable.
Verify the truss is determinate or indeterminate in case the truss is stable.
Find the degree of indeterminacy in case the given truss is statically indeterminate.
(g)
Answer to Problem 1P
The plane truss is stable and determinate.
Explanation of Solution
Refer the Figure of the given plane truss.
The number of the bars in the plane truss is
The number of reaction is
The number of the joints in the plane truss is
Substitute the values of b, r, and n with Equation (4).
Thus, the plane truss is stable and determinate.
(h)
Categorize the given truss is stable or unstable.
Verify the truss is determinate or indeterminate in case the truss is stable.
Find the degree of indeterminacy in case the given truss is statically indeterminate.
(h)
Answer to Problem 1P
The plane truss is geometrically unstable.
Explanation of Solution
Refer the Figure of the given plane truss.
The number of the bars in the plane truss is
The number of reaction is
The number of the joints in the plane truss is
The reactions are concurrent.
Refer to the given figure, all the supports are roller. So the structure is geometrically unstable.
Thus, the plane truss is geometrically unstable.
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