(a)
The required diameter of group
Answer to Problem 8.2.7P
The required diameter of the bolt by elastic analysis using LRFD is
Explanation of Solution
Given data:
The live load is
The dead load is
Concept Used:
Write the equation of nominal bolt area.
Here, the diameter of bolt is
Calculation:
Write the equation to calculate the factored load for LRFD.
Here, the dead load is
Substitute
Determine the centroid with respect to the lower left bolt.
Write the equation to calculate the distance of centroid in
Here, the number of bolts is
Substitute the values in Equation (III).
Write the equation to calculate the distance of the centroid in
Substitute the values in Equation (IV).
Write the expression to calculate the load applied in the
Here, the total load is
Substitute
Write the expression to calculate the load applied in the
Here, the and load component in
Substitute
Write the equation to calculate the horizontal direct shear component.
Here, the load in
Substitute
Write the equation to calculate the vertical direct shear component.
Here, the load in
Substitute
Calculate the horizontal and vertical components of loads due to eccentricity.
Calculate the distance of the load from centroid of connection.
Here, the eccentricity in
Write the expression for the moment for
Here, moment generated is
Substitute
Write the expression for the moment for
Here, moment generated is
Substitute
Write the expression for the moment for
Here, the total moment generated is
Substitute
Write the equation to calculate the total fastener force.
Here, the total fastener force is
Write the equation to calculate the
Here, the horizontal direct shear component is
Write the equation to calculate the
Here, the vertical direct shear component is
The top right bolt is critical, thus check for its safety.
Calculate the distance of the bolt from the centroid.
Here, the distance of the top right bolt from the centroid in the x and y directions are
Write the equation to calculate the load coming on the critical bolt in x direction due to eccentricity.
Substitute
Write the equation to calculate the load coming on critical bolt in y direction due to eccentricity.
Substitute
Calculate the
Substitute
Calculate the
Substitute
Calculate the total fastener force.
Substitute
Check the safety for the bottom right bolt.
Calculate the distance of the bolt from the centroid.
Calculate the load coming on the critical bolt in x direction due to eccentricity.
Substitute
Calculate the load coming on critical bolt in y direction due to eccentricity.
Substitute
Calculate the
Substitute
Calculate the
Substitute
Calculate the total fastener force.
Substitute
Therefore, the total shear force in the fastener is
Write the equation to calculate the nominal shear capacity of bolt.
Here, the nominal shear capacity is
Substitute
Calculate the diameter of bolt.
Substitute
Therefore, adopt the bolt diameter of
Check for safety:
Write the equation to calculate the bearing deformation strength of the bolt.
Here, the bearing deformation strength is
Assume A36 steel and the value of
Assume the thickness of the plate is
Calculate the bearing deformation strength of bolt.
Substitute
Write the equation to calculate the tear-out strength of inner bolt.
Here, the tear-out strength of inner bolt is
Write the equation to calculate the clear distance for edge bolt.
Here, the bolt edge distance is
Write the equation to calculate the hole diameter.
Calculate the clear distance for edge bolt.
Substitute
Calculate the tear-out strength of inner bolt.
Substitute
Write the equation to calculate the tear-out strength of edge bolt.
Here, the tear-out strength of edge bolt is
Write the equation to calculate the clear distance for edge bolt.
Here, the spacing between bolts is
Substitute
Calculate the tear-out strength of edge bolt.
Substitute
The minimum of Equations (XXII), (XIX) and (XVIII) is the value of
Calculate the design of strength of bolt by substituting
The strength is greater than the design strength.
Therefore, adopt
Conclusion:
Thus, the size of bolt is
(b)
The size of bolt by elastic analysis using ASD.
Answer to Problem 8.2.7P
The size of bolt by elastic analysis using ASD is
Explanation of Solution
Calculation:
Write the equation to calculate the factored load.
Here, the dead load is
Substitute
Write the expression to calculate the load applied in
Here, the total load is
Substitute
Write the expression to calculate the load applied in
Here, the and load component in
Substitute
Calculate the horizontal direct shear component.
Substitute
Calculate the vertical direct shear component.
Substitute
Write the expression for the moment for
Here, moment generated is
Substitute
Write the expression for the moment for
Here, moment generated is
Substitute
Write the expression for the moment for
Here, the total moment generated is
Substitute
Check the safety for the bottom right bolt.
Calculate the distance of the bolt from the centroid.
Calculate the load coming on the critical bolt in x direction due to eccentricity.
Substitute
Calculate the load coming on critical bolt in y direction due to eccentricity.
Substitute
Calculate the
Substitute
Calculate the
Substitute
Calculate the total fastener force.
Substitute
Write the equation to calculate the nominal shear capacity of bolt.
Here, the nominal shear capacity is
Substitute
Calculate the diameter of bolt.
Substitute
Therefore, adopt the bolt diameter of
Check for safety:
Calculate the bearing deformation strength of bolt.
Substitute
Calculate the hole diameter.
Calculate the clear distance for edge bolt.
Substitute
Calculate the tear-out strength of inner bolt.
Substitute
Calculate the clear distance for edge bolt.
Substitute
Calculate the tear-out strength of edge bolt.
Substitute
The minimum of Equations (XXII), (XIX) and (XVIII) is the value of
Calculate the allowable strength of bolt by substituting
The strength is greater than the design strength.
Therefore, adopt
Conclusion:
Thus, the size of bolt is
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Chapter 8 Solutions
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