(a)
The design strength using Load and Resistance Factor Design(LRFD).
Answer to Problem 3.2.1P
Explanation of Solution
Given:
A36 steel PL
The effective area,
Concept Used:
Write the expression for the factored strength in yielding.
Write the expression for the factored strength in rupture.
Herethe strength of the material is
The design strength of LRFD is the minimum of Equation (I) and (II).
Write the expression for the nominal strength in yielding.
Here, the yield strength in yielding is
Write the expression for the gross area of the member.
Here, the length of the member is
Write the expression for the nominal strength in rupture.
Here, the yield strength in rupture is
Given that,
Here, the area of the holes is
Write the expression for the area of the holes.
Here, the diameter of the holes is
Write the expression for the diameter of the holes.
Here, the diameter of the bolts is
For the A36 steel resistance factors and the yield strength values are,
Calculation:
Calculate the gross area.
Substitute
Calculate the diameter of holes.
Substitute
Calculate the area of holes.
Substitute
Calculate the effective area.
Substitute
Calculate the yielding strength.
Substitute
Calculate the strength at rupture.
Substitute
Calculate the design strength in yielding.
Substitute
Calculate the design strength in rupture.
Substitute
Conclusion:
Compare the design strengthin yielding and rupture. The design strength using LRFD is the smaller of the two.
Thus, the design strength using LRFD is
(b)
The allowable strength usingAllowable Strength Design (ASD).
Answer to Problem 3.2.1P
The allowable strength using ASD is
Explanation of Solution
Write the expression for the allowable strength inyielding.
Here, the safety factor in yielding is
Write the expression for the allowable strength for rupture.
Here, the safety factor in rupture is
The allowable strength is the minimum of Equation (IX) and (X).
Calculation:
Calculate the allowable strength in yielding.
Substitute
Calculate the allowable strength in rupture.
Substitute
Conclusion:
Compare the allowable strength in yielding and rupture. The smaller values are the allowable strength using ASD.
Thus, the allowable strength using ASD is
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Chapter 3 Solutions
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