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Structural Analysis
Structural Analysis
99 SOLVED PROBLEMS
Question: 3.1.1
Figure 3.1-2 shows a cube of sides 1 m acted on by eight forces and a moment as shown. Determine the magnitude and direction of the resultant force R and the coordinates (x, y, z) of the point at which R intersects the face OACB. Is there a resultant moment in addition to the resultant force R ? ...
Verified Answer:
\qquad \begin{matrix} \qquad \sum{P_{x}} &a...
Question: 12.9.1
Prepare a flow chart to replace Step 3 to Step 9 of that in Subsection 12.9(c). ...
Verified Answer:
In Subsection 12.9(c), a flow chart is given for b...
Question: 10.3.2
Figure 10.3-4 shows a portal frame ABCD; it may be assumed that the horizontal member is infinitely stiff and that the vertical members have negligible mass compared with that of the horizontal member. If there is no damping, determine (a) the natural frequency ƒ and the natural period T (b) the ...
Verified Answer:
(1) From Section 5.2, Eqn 5.2-1, the stiffnesses o...
Question: 3.5.3
Figure 3.5-3(a) shows a determinate space truss made up of horizontal, vertical, and inclined members. The horizontal members and the vertical members are all of equal length. Member GJ is a diagonal of a cube, while all other inclined members are diagonals of equal squares. The truss is acted on ...
Verified Answer:
By Rule 1, member 1 is unstressed; similarly membe...
Question: 2.6.2
Briefly explain the basis of the method of joints for statically determinate trusses. Using the method of joints, determine analytically the reactions and member forces in the truss in Fig. 2.6-1 (a). ...
Verified Answer:
If there are j joints in a truss, then since there...
Question: 2.6.1
Figure 2.6-1(a) shows a statically determinate truss acted on by a force F applied at joint B. Using the method of joints, determine graphically the axial forces in all the members and the support reactions at A and D. ...
Verified Answer:
Since each joint is in equilibrium under the actio...
Question: 14.3.1
Derive an expression for the bending moment in a rectangular section when the stress distribution is partly plastic and partly elastic (Fig. 14.3-3). ...
Verified Answer:
Force in each plastic zone =
\sigma _{y}b\l...
Question: 14.10.3
Using the method of combination of mechanisms, determine the shakedown load factor λ for the uniform frame in Fig. 14.10-6(a) if the load H can vary at random within the range 0 to 10λ kN and the load V can vary at random within the range 0 to 15λ kN. The plastic moment of resistance of each ...
Verified Answer:
Three collapse mechanisms can be identified. These...
Question: 14.10.2
Using Eqn 14.10-26, obtain an upper bound on the shakedown load factor for the uniform two-span beam in Fig. 14.10-2, if the loads Pand Q may each vary at random within the range 0 to λ Mp. ...
Verified Answer:
Consider the mechanism in Fig. 14.10-5. The elasti...
Question: 14.8.3
Using the safe theorem, given an alternative solution to Example 14.8-2. ...
Verified Answer:
Fig. 14.8-4 shows a bending moment diagram obtaine...
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