Concept explainers
Classify each of the structures shown as completely, partially, or improperly constrained; if completely constrained, further classify as determinate or indeterminate. (All members can act both in tension and in compression.)
(a)
Classify the given structure as completely, partially, or improperly constrained and if completely constrained, further classify as determinate or indeterminate.
Answer to Problem 6.70P
The given structure is completely constrained and determinate.
Explanation of Solution
The structure is shown in Fig. P6.70 (a). The free-body diagram of the truss is given in Figure 1.
Write the condition for a truss to be completely constrained.
Here,
Write the condition for a truss to be partially constrained.
Write the expression for a truss to be indeterminate.
Write the expression for the condition for equilibrium.
Here,
Conclusion:
For the given truss,
Compute
Compute
So, for the given system,
Apply the condition for equilibrium in equation (IV) about various points of the structure in the free-body diagrams
Apply the condition for equilibrium in equation (V) about various points of the structure in the free-body diagrams
Since each section is a simple truss with reactions determined, the given structure is completely constrained and determinate.
Therefore, the given structure is completely constrained and determinate.
(b)
Classify the given structure as completely, partially, or improperly constrained and if completely constrained, further classify as determinate or indeterminate.
Answer to Problem 6.70P
The given structure is partially constrained.
Explanation of Solution
The structure is shown in Fig. P6.70 (b). It is a non-simple truss.
From equations (I), and (II), the conditions for the state of constrain of the structure is as follows,
Conclusion:
For the given truss,
Compute
Compute
So, for the given system,
Therefore, the given structure is partially constrained.
(c)
Classify the given structure as completely, partially, or improperly constrained and if completely constrained, further classify as determinate or indeterminate.
Answer to Problem 6.70P
The given structure is improperly constrained and indeterminate.
Explanation of Solution
The structure is shown in Fig. P6.70 (c). The free-body diagram of the truss is given in Figure 2.
From equations (I), and (II), the conditions for the state of constrain of the structure is as follows,
Conclusion:
For the given truss,
Compute
Compute
It is clear that for the given system, the condition in equation (I) is satisfied, but the horizontal reaction forces
Therefore, the given structure is improperly constrained and indeterminate.
Want to see more full solutions like this?
Chapter 6 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
Additional Engineering Textbook Solutions
Mechanics of Materials (10th Edition)
Automotive Technology: Principles, Diagnosis, And Service (6th Edition) (halderman Automotive Series)
Statics and Mechanics of Materials
Degarmo's Materials And Processes In Manufacturing
Engineering Mechanics: Statics
Fluid Mechanics Fundamentals And Applications
- Problem 07.093.b - Maximum tension of cable with level supports Determine the maximum tension in the cable.arrow_forwardA bar AE is in equilibrium under the action of the five forces shown. Determine P, R and T.arrow_forwardThe structure shown is composed of an AGJ truss and a KLMO truss connected by the AL link. If it is known that P = 2 kN; R = 5kN; a = 1.5 m and b = 2m, determine:to. The value of the force Q, necessary to keep the system in equilibrium.b. The axial loads of the reinforcement elements. (need free body diagrams)arrow_forward
- The truss shown is supported by a hinge at A and a roller at G. Determine all bar forces of the following using the method of Joints: AB, AH, BC, BH, CH, CG, CF, CD, DE, DF, EF, FG, GHarrow_forwardSolve Prob. 4.123, assuming that the 1.8-kN load is applied at C.(Reference to Problem 4.123):The rigid L-shaped member ABC is supported by a ball-and-socket joint at A and by three cables. If a 1.8-kN load is applied at F , determine the tension in each cable.arrow_forwardUsing the method of joints, determine the force in each member of the truss shown. State whether each member is in tension or compression.arrow_forward
- International Edition---engineering Mechanics: St...Mechanical EngineeringISBN:9781305501607Author:Andrew Pytel And Jaan KiusalaasPublisher:CENGAGE L