# Engineering Mechanics & Design of Steel Structures : Plastic Analysis

By Sajal Gupta|Updated : March 10th, 2022

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### Plastic Analysis

Plastic Beam & Frame Analysis PDF by NPTEL

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Plastic Sections Modulus

• Plastic Section Modulus

Shape Factor (∝)

Where Zy is elastic section modulus

Load Factor = Factor of safety x Shape factor

λ = FS × α

Shape factors for different shapes

Reserve Strength (Ψ)

• It is the ratio of the ultimate load Wu to the load at first yield Wy of the structure.

Length of a Plastic hinge (Lp)

• It is the length of the beam over which the moment is greater than the yield moment (My).

(a) For simply supported beam carrying a concentrated load, length of plastic hinge is given by
(for rectangular section)

(for I section)
(b) For simply support beam carrying UDL length of plastic hinge is given by

Where ∝ is shape factor and L is the total length of the beam.

• Simply supported beam with the concentrated load at the center

• Simply supported beam with the uniformly distributed load

• Propped cantilever with a concentrated load at the center

• Propped cantilever with a uniformly distributed load

• Fixed beam with a concentrated load at the center

• Fixed beam with the uniformly distributed load

• Continuous beam with a uniformly distributed load

The positions of the plastic hinges are one at the support B and one on each side of the central support at a distance of 0.414L from A & C.

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