Concept explainers
Two 89 × 64-mm angles are bolted together as shown for use as a column of 2.4-m effective length to carry a centric load of 325 kN. Knowing that the angles available have thicknesses of 6.4 mm, 9.5 mm, and 12.7 mm, use allowable stress design to determine the lightest angles that can be used. Use σY = 250 MPa and E = 200 GPa.
Fig. P10.84
Find the lightest angles that can be used.
Answer to Problem 84P
The lightest angle that can be used for the design is
Explanation of Solution
Given information:
The effective length of the column is
The allowable yield strength of the steel is
The modulus of elasticity of the steel is
The centric load acting in the column is
Calculation:
Consider the thickness of the angle section as 9.5 mm.
Refer to Appendix C “Properties of Rolled-Steel Shapes” in the textbook.
For
The cross sectional area of the angle (A) is
The moment of inertia in x-axis is
The moment of inertia in y-axis is
The centroid distance from the flange in x-axis is
The area of the two angle section is
The moment of inertia in x-axis is
Find the moment of inertia in y-axis using the relation.
Substitute
The minimum moment of inertia is
Find the minimum radius of gyration (r) using the relation.
Substitute
Find the slenderness ratio
Here, the modulus of elasticity of the material is E and the allowable yield strength is
Substitute 200 GPa for E and 250 MPa for
Find the ratio of effective length
Find the effective stress
Substitute 200 GPa for E and 97.22 for
Find the critical stress
Substitute 250 MPa for
Calculate the allowable stress
Substitute 151.472 MPa for
Calculate the allowable load
Substitute 90.702 MPa for
The centric load is greater than the allowable load. Hence, the design is unsafe.
Consider the thickness of the angle section as 12.7 mm.
Refer to Appendix C “Properties of Rolled-Steel Shapes” in the textbook.
For
The cross sectional area of the angle (A) is
The moment of inertia in x-axis is
The moment of inertia in y-axis is
The centroid distance from the flange in x-axis is
The area of the two angle section is
The moment of inertia in x-axis is
Find the moment of inertia in y-axis using the relation.
Substitute
The minimum moment of inertia is
Find the minimum radius of gyration (r) using the relation.
Substitute
Find the slenderness ratio
Here, the modulus of elasticity of the material is E and the allowable yield strength is
Substitute 200 GPa for E and 250 MPa for
Find the ratio of effective length
Find the effective stress
Substitute 200 GPa for E and 95.12 for
Find the critical stress
Substitute 250 MPa for
Calculate the allowable stress
Substitute 154.753 MPa for
Calculate the allowable load
Substitute 92.667 MPa for
The centric load is less than the allowable load. Hence, the design is unsafe.
Therefore, the lightest angle that can be used for the design is
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Chapter 10 Solutions
EBK MECHANICS OF MATERIALS
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