Concept explainers
The steel bar AB has a
Fig. P10.41
Find the increase in temperature.
Answer to Problem 41P
The increase in temperature required for the bar to make contact with the point C is
Explanation of Solution
The centricity of the load in the column is
The distance between the bar and the pins is
The modulus of elasticity of the steel bar is
The length of the column is
The coefficient of thermal expansion is
The dimension of the square cross section is
Find the moment of inertia of the square cross section (I) using the equation.
Here, the dimension of the square cross section is a.
Substitute
The effective length of the column
Determine the critical load
Here, the modulus of elasticity is E.
Substitute
Determine the axial load P using the equation.
Here, the deflection of the column is
Substitute 0.01 in. for d, 0.03 in. for e, and 7,370 lb for
Find the cross sectional area of the square cross section (A) as follows;
Substitute
Consider without the eccentricity of the load to find the temperature change;
Find the total elongation using the relation.
Here, the elongation due to thermal stress is
The total elongation in the column should be zero.
Substitute 1,560.2 lb for P,
Consider the eccentricity to find the temperature change;
Find the total elongation in the column using the relation.
Refer to Equation (10.26) in the textbook.
Apply the elastic curve equation;
Differentiate the equation.
When the distance
Refer to Equation (10.6) in the textbook.
The critical load is given by the equation.
Substitute
Substitute
Substitute 1,560.2 lb for P, 7,370 lb for
The smallest change in temperature controls the design.
The smallest temperature change occurs when the eccentricity is not considered.
Therefore, the increase in temperature required for the bar to make contact with the point C is
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Chapter 10 Solutions
Mechanics of Materials, 7th Edition
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