The three beams shown have approximately the same cross-sectional area. Beam 1 is a W 14 X 82 with flange plates; beam 2 consists of a web plate with four angles; and beam 3 is constructed of 2 C shapes with flange plates.
- Which design has the largest moment capacity?
- Which has the largest shear capacity?
- Which is the most economical in bending?
- Which is the most economical in shear?
Assume allowable stress values are: = 18 ksi and ra=11 ksi. The most economical beam is that having the largest capacity-to-weight ratio. Neglect fabrication costs in answering parts (c) and (d) above. Note: Obtain the dimensions and properties of all rolled shapes from tables in Appendix F.
The beam of the largest momentum capacity.
Answer to Problem 5.11.11P
The beam of the largest momentum capacity is beam-1.
Explanation of Solution
Given information:
The allowable normal stress is
Write the expression for the total moment of inertia of the beam-1.
Here, the total moment of inertia of the beam-1.is
Write the expression for the total height of the beam-1.
Here, the total height of the beam-1 is
Write the expression for the total area of the beam-1.
Here, the total area of the beam-1.is
Write the expression for the section of the modulus of the beam-1.
Here, the section of the modulus of the beam-1
Write the expression for the total moment of inertia of the beam-2.
Here, the total moment of inertia of the beam-2 is
Write the expression for the total area of the beam-2.
Here, the total area of the beam-2 is
Write the expression for the section of the modulus of the beam-2.
Here, the section of the modulus of the beam-2 is
Write the expression for the total height of beam-3.
Here, the total height of beam-3 is
Write the expression for the total moment of inertia of the beam-3.
Here, the total moment of inertia of the beam-2 is
Write the expression for the total area of the beam-3.
Here, the total area of the beam-3 is
Write the expression for the section of the modulus of the beam-3.
Here, the section of the modulus of the beam-3
Calculation:
Refer Table-F-1(a) “Properties of wide flange section” to obtain
Substitute
Substitute
Substitute
Substitute
Refer Table-F-4(a) “Properties of wide equal legs L-shape channel”
Substitute
Substitute
Substitute
Refer Table-F-3(a) “Properties of C-shape channel” for
Substitute
Substitute
Substitute
Substitute
Since stress due to moment is inversely proportional to section modulus, therefore the beam which has the highest section modulus will have the highest capacity.
The value of the section modulus of the beam-1 is highest i.e.,
Conclusion:
The beam of the largest momentum capacity. is beam-1.
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