Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)

Load Factor

• The load factor (λ)
  λ = Collapse load / Service load = P_c / P

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Plastic Sections Modulus

• Plastic Section Modulus
  

Shape Factor (∝)
∝ = M_P / M_y = Z_P / Z_y

Where Z_y is the elastic section modulus
Load factors
(λ) = P_c / P

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 W_u to the load at first yield W_y of the structure.
  ψ = W_u / W_y

Length of a Plastic hinge (L_p)

• It is the length of the beam over which the moment is greater than the yield moment (M_y).
  (a) For simply supported beam carrying a concentrated load, length of plastic hinge is given by L_p = L/3 (for rectangular section)
  (b) For simply supported beam carrying UDL length of plastic hinge is given by
  Where ∝ is the shape factor, and L is the total length of the beam.
• The length of the plastic hinge depends on loading and geometry.

• 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 eccentric loading

• Fixed beam with the uniformly distributed load

• Fixed beam with hydrostatic loading

• Continuous beam with a uniformly distributed load

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