(a)
The available shear strength of the connection based on Allowed Stress Design.
Answer to Problem 8.6.3P
The available shear strength of the connection based on Allowed Stress Design.
is
Explanation of Solution
Given:
A
The
Calculation:
The available shear strength of the connections is least of the following,
- Strength of the bolt.
- Plates shear yielding strength.
- Plate shear rupture strength.
- Plates block shear strength.
- Strength of the weld.
Write the expression to obtain the bolt shear strength.
Here, the cross section area of the unthreaded part of the bolt is
Substitute
The shear strength of the
Write the expression to obtain the bearing strength of the bolts on the plate.
Here, the safety factor is
Substitute
Thus,
The bearing strength for the two bolts adjacent to the plate.
Write the expression to obtain the bearing strength of the bolts other than on the plate.
Here, the safety factor is
Substitute
Thus,
The bearing strength for the two such bolts is,
Thus, the total bearing strength of the bolts is:
Thus, the bolt strength is least of the shear strength and bearing strength of the bolts.
From Equations (II) and (V),
Write the expression to obtain the plate shear yielding strength.
Here, the gross cross section area of the plate perpendicular to the applied load is
Substitute
Write the expression to obtain the shear rupture strength of the plate.
Here, the net area along the shear surface is
Substitute,
Write the expression to obtain the block shear strength of the plate.
Here, the net area along the shear surface is
Substitute
Thus,
Write the expression to obtain the design shear strength of weld.
Here, the size of the fillet weld is
Substitute
Further solve the above equation.
For
Write the expression to obtain the shear yielding strength for the base metal for
Here, the thickness of the base metal is
Substitute
Write the expression to obtain the shear rupture strength of the base metal.
Here, the thickness of the base metal is
Substitute
Write the expression to obtain the yielding strength for the base metal.
Here, the thickness of the base metal is
Substitute
From Equation (VI), (VIII), (X) and (XXI), the least value will be the available shear strength of the connections.
Thus,
Conclusion:
Thus, the available shear strength of the connection is
(b)
The flexural strength of the member based on Allowed Stress Design.
Answer to Problem 8.6.3P
The available flexural strength of the member based on Allowed Stress Design.
is
Explanation of Solution
Calculation:
The available flexural strength of the connections is least of the following,
- Strength of the bolt.
- Tension on gross section of the plate.
- Tension on net section of the plate.
- The block shear of the flange plate.
- The block shear of the beam flange.
- The compression of the bottom flange plate.
Write the expression to obtain the tension force due to yielding of the gross section area of the plate.
Here, the gross sectional area of the plate is
Substitute,
Write the expression to obtain the tension rupture strength of the plate.
Here, the net area of the plate is
Substitute,
Write the expression to obtain the bolt shear strength.
Here, the cross section area of the unthreaded part of the bolt is
Substitute
The shear strength of the
Write the expression to obtain the bearing strength of the bolts on the plate.
Here, the safety factor is
Substitute
Thus,
The bearing strength for the
Write the expression to obtain the bearing strength of the bolts other than on the plate.
Here, the safety factor is
Substitute
Thus,
The bearing strength for
Thus, the total bearing strength of the bolts is:
Thus, the bolt strength is least of the shear strength and bearing strength of the bolts.
From Equation (XXVII) and (XXX),
Write the expression to obtain the block shear strength of the plate.
Here, the net area along the shear surface is
Substitute
Thus,
Write the expression to obtain the block shear strength of the beam flange.
Here, the net area along the shear surface is
Substitute
Thus,
Write the expression to obtain the compressive strength of the member.
Here, the safety factor for compression is
Substitute,
From Equations (XXIII), (XXV), (XXXI), (XXXV) and (XXXVII), the least value will be the tension at the net section as
Thus,
Write the expression to obtain the moment transferred by flange plate.
Here, lever arm distance is
Substitute
Conclusion:
Thus, the available flexural strength of the member is
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