Concept explainers
An L-shaped reinforced concrete slab 12 Ft X 12 ft, with a 6 Ft X 6 ft cut-out and thickness t = 9.0 in, is lifted by three cables attached at O, B, and D, as shown in the figure. The cables are are combined at point Q, which is 7.0 Ft above the top of the slab and directly above the center of mass at C. Each cable has an effective cross-sectional area of Ae= 0.12 in2.
(a) Find the tensile force Tr(i = 1, 2, 3) in each cable due to the weight W of the concrete slab
(ignore weight of cables).
(b) Find the average stress ov in each cable. (See Table I-1 in Appendix I for the weight density of reinforced concrete.)
(c) Add cable AQ so that OQA is one continuous cable, with each segment having Force T, which is connected to cables BQ and DQ at point Q. Repeat parts (a) and (b). Hini: There are now three Forced equilibrium equations and one constrain equation, T1= T4.
(a)
Tensile force T in each cable due to weight.
Answer to Problem 1.4.13P
Tensile force T is:
Explanation of Solution
Given Information:
You have the following figure with all relevant information:
Thickness (t) is 9 in.
Calculation:
Consider the free body diagram as:
To calculate external reaction force F, take equilibrium of forces as:
The following force acts on point Q:
Take equilibrium of forces at Q as:
Solve the above equation to get:
Conclusion:
Therefore, the correct answers are
(b)
Average stress in each cable.
Answer to Problem 1.4.13P
Stress in each cable is
Explanation of Solution
Given Information:
You have following figure with all relevant information:
Thickness (t) is 9 in. and cross-sectional area of each cable is
Calculation:
Consider the free body diagram as,
To calculate external reaction force F, take equilibrium of forces as,
The following forces acts on point Q:
Take equilibrium of forces at Q as:
Solve the above equation to get,
Calculate stress as,
Conclusion:
Therefore, the correct answer is:
(c)
Tensile force and average stress in each cable.
Answer to Problem 1.4.13P
Stress in each cable is:
Explanation of Solution
Given Information:
You have following figure with all relevant information:
Thickness (t) is 9 in. and cross-sectional area of each cable is
Calculation:
Consider the free body diagram as,
To calculate external reaction force F, take equilibrium of forces as:
The following force acts on point Q:
Take equilibrium of force at Q as:
Solve the above equation along with
Calculate stress as:
Conclusion:
Therefore, the correct answers are:
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Chapter 1 Solutions
Mechanics of Materials (MindTap Course List)
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- Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning