(a)
The maximum factored load using Load and Resistance Factor Design (LRFD).
Answer to Problem 3.5.4P
The maximum factored load using LRFD is
Explanation of Solution
Given:
The following figure shows the A36 steel connection with
Figure-(1)
Concept Used:
Write the expression for the factored strength in yielding.
Write the expression for the factored strength in rupture.
Here, the factored yielding strength of the material is
Write the expression for block shear.
Write the expression for the upper limit of block shear.
Here, the upper limit is
Write the expression for the design block shear strength.
Here the design block shear strength, the minimum of Equation (III) and (IV), is
The maximum factored load is the minimum of Equation (I), (II), and (V).
Write the expression for the nominal strength in yielding for the tension member.
Here, the yield strength in yielding is
Write the expression for the nominal strength in rupture for the tension member.
Here, the yield strength in rupture is
Write the expression for the effective area.
Here, the area reduction factor is
Write the expression for the area reduction factor.
Here the distance from the centroid of the connected area
Write the expression for the net area of the tension member.
Here, the thickness of the tension member is
Write the expression for the diameter of the holes.
Here the diameter of the bolts is
Calculation:
Calculate the nominal shear strength of the tension member in yielding.
Substitute
Calculate the diameter of the holes.
Substitute
Calculate the net area of the tension member.
Substitute
Calculate the length of the connection.
Calculate the area reduction factor.
Substitute
Calculate the effective area of the member.
Substitute
Calculate the nominal shear strength of the tension member in rupture.
Substitute
Calculate the net area along the shear surface of the tension member.
Calculate the net area along the tension surface of the tension member.
Calculate the gross area along the shear surface in the gusset plate.
Calculate the net area along the shear surface of the gusset plate.
Substitute further.
Calculate the net area along the tension surface of the gusset plate.
Calculate the shear strength for the tension member.
Substitute
Calculate the upper limit.
Substitute
The value of the shear is larger than the upper limit. Hence, it is not feasible.
Adopt the shear strength of the tension member to be
Calculate the shear strength for the gusset plate.
Substitute
Calculate the upper limit
Substitute
The value of the shear is larger than the upper limit. Hence, it is not feasible.
Adopt the shear strength of the gusset plate to be
Compare the shear strength of the tension member and that of the gusset plate.
Thus the block shear strength is
Calculate the design block shear strength of the connection.
Calculate the factored yielding strength.
Substitute
Calculate the factored rupture strength.
Substitute
Calculate the factored strength of block shear.
Substitute
Conclusion:
Thus, the maximum factored load is
(b)
The allowable block shear strength of the connection.
Answer to Problem 3.5.4P
The allowable block shear strength of the connection is
Explanation of Solution
Concept used:
Write the expression for the factored design block shear strength.
Here the safety factor is
Calculation:
Calculate the allowable block shear strength of the connection.
Calculate the allowable yielding strength.
Substitute
Calculate the allowable rupture strength.
Substitute
Calculate the factored strength of block shear.
Substitute
Conclusion:
Thus, the maximum allowable block shear strength of the connection is
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Chapter 3 Solutions
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