Concept explainers
Space frame A BCD is clamped at A, except it is Free to translate in the .v direction. There is also a roller support at D, which is normal to line CDE. A triangularly distributed Force with peak intensity q0 = 75 N/m acts along AB in the positive - direction. Forces Px= 60 N and Pz = = 45 N are applied at joint C, and a concentrated moment My = 120 N . m acts at the mid-span of member BC.
(a) Find reactions at supports A and I).
(b) Find internal stress resultants N. E’I T, and .11 at the mid-height of segment AB.
(a)
Reactions at support A,D.
Answer to Problem 1.3.30P
The correct answers are:
Explanation of Solution
Given Information:
You have following figure with all relevant information,
and
Draw free body diagram of joints and use equilibrium of forces to determine the unknowns.
Calculation:
Draw free body diagram as shown in the following figure,
The forces and corresponding position vectors are,
Force | Position vector |
|
|
|
|
|
|
|
|
Take equilibrium of forces vector form,
The vector equation yields three equations in components form as below,
Solve the three equations to get
Now, calculate components of D as,
Now take equilibrium of moments about A in vector form as,
Evaluate the cross products to get,
Conclusion:
Therefore the forces and moments are:
(b)
Internal stress resultants N,V,T and M at mid height of AB.
Answer to Problem 1.3.30P
The correct answers are:
Explanation of Solution
Given Information:
You have following figure with all relevant information,
and
Draw free body diagram of joints and use equilibrium of forces to determine the unknowns.
Calculation:
Draw free body diagram as shown in the following figure,
The forces and corresponding position vectors are,
Force | Position vector |
|
|
|
|
|
|
|
|
Take equilibrium of forces vector form,
The vector equation yields three equations in components form as below,
Solve the three equations to get
Now, calculate components of D as,
Now take equilibrium of moments about A in vector form as,
Evaluate the cross products to get,
Calculation internal stress resultants at mid point of AB :
Consider the following free body diagram,
Analyze the lower part of the above free body diagram,
Take equilibrium of forces in vector form,
Solve the above equation in component form to get,
Take equilibrium of moments about A in vector form as,
Evaluate the cross products and solve to get,
Equivalent moment,
Conclusion:
Thus the internal stress resultants 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