Concept explainers
Determine the shape factor for the wide-flange beam.
R6–1
Answer to Problem 1RP
The shape factor for the wide-flange beam is
Explanation of Solution
Determination of Elastic moment:
Moment of inertia:
Show the free-body diagram of the beam as in Figure 1.
Consider the beam as rectangular and determine the moment of inertia for rectangular section and deduct the moment of inertia of the two smaller rectangular portions.
Determine the moment of inertia of the I-section using the formula.
Here, B is width of rectangular section, D is depth of large rectangular section, b is depth of small rectangular section, and d is depth of small rectangular section.
Substitute 180 mm for B, 220 mm for D, 75 mm for b, and 180 mm for d in Equation (1).
Elastic moment:
Determine the elastic moment using the equation.
Here,
Substitute
Determination of plastic moment:
Show the free-body diagram of the profile view of the I-beam as in Figure 2.
Determine the plastic moment in the I-section using the equation.
Here,
Substitute 180 mm for
Shape factor:
Determine the shape factor for the I-section using the formula.
Substitute
Thus, the shape factor for the wide-flange beam is
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Chapter 6 Solutions
Mechanics of Materials
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