Concept explainers
The American Standard rolled-steel beam shown has been reinforced by attaching to it two 16 × 200-mm plates, using 18-mm-diameter bolts spaced longitudinally every 120 mm. Knowing that the average allowable shearing stress in the bolts is 90 MPa, determine the largest permissible vertical shearing force.
The largest permissible vertical shearing force.
Answer to Problem 5P
The largest permissible vertical shearing force is
Explanation of Solution
Given information:
The diameter of bolt is
The longitudinal spacing is
The average shearing stress in the bolts is
Calculation:
Provide the section properties of the rolled steel beam
The area of the section is
The moment of inertia of the section
The Overall depth of the member
Calculate the moment of inertia as shown below.
Here, b is the breadth of the beam, h is the height of the beam, A is the area of the beam, and
For the top plate.
Calculate the area
Calculate the location of the centroid
Similarly calculate the moment of inertia for the bottom plate and rolled steel beam
Part | Area, | Moment of Inertia, | ||
Top plate | ||||
Bottom plate |
Calculate the moment of inertia for the whole section as shown below.
Calculate the first moment of area
Substitute
Calculate the area of bolt as shown below.
Here,
Substitute
Calculate the force acting on the bolt
Here,
Substitute
Calculate the horizontal shear per unit length as shown below.
Substitute
Calculate the vertical shearing force (V) as shown below.
Substitute
Therefore, the largest permissible vertical shearing force is
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Chapter 6 Solutions
Mechanics of Materials, 7th Edition
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