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Load Factor
- The load factor (λ)
λ = Collapse load / Service load = Pc / P
Saving in material
% saving in material
Plastic Sections Modulus
- Plastic Section Modulus
Shape Factor (∝)
∝ = MP / My = ZP / Zy
Where Zy is the elastic section modulus
Load factors
(λ) = Pc / 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 Wu to the load at first yield Wy of the structure.
ψ = Wu / Wy
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 Lp = 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.
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FAQs on Plastic Analysis - Design of Steel Structures - Civil Engineering (CE)
| 1. What is plastic analysis in civil engineering? |  |
Ans. Plastic analysis is a method used in civil engineering to determine the strength and behavior of structures beyond their elastic limit. It considers the plastic deformation of materials and analyzes the structure's ability to redistribute stresses and achieve a stable collapse mechanism.
| 2. What are the advantages of plastic analysis in civil engineering? | |
Ans. Plastic analysis offers several advantages in civil engineering. It provides a more realistic assessment of a structure's strength and deformation capacity compared to traditional elastic analysis. It allows for the design of structures that can undergo large deformations without collapsing, leading to more efficient and economical designs.
| 3. How is plastic analysis different from elastic analysis in civil engineering? | |
Ans. Plastic analysis differs from elastic analysis in civil engineering as it considers the behavior of materials beyond their elastic limit. Elastic analysis assumes that materials will return to their original shape once the applied load is removed, whereas plastic analysis acknowledges that materials may undergo permanent deformation but can still support loads without failure.
| 4. What are the limitations of plastic analysis in civil engineering? | |
Ans. Plastic analysis has certain limitations in civil engineering. It is more complex and time-consuming compared to elastic analysis. It requires accurate material properties and assumptions about the structure's behavior, which may be challenging to obtain. Additionally, plastic analysis may not accurately predict the behavior of structures subjected to dynamic or seismic loads.
| 5. How is plastic analysis used in the design of structures? | |
Ans. Plastic analysis is used in the design of structures to ensure their strength and stability. It helps determine the critical load at which plastic deformation occurs and identifies the collapse mechanism. Engineers can then design structures to withstand these loads, allowing for the redistribution of stresses and preventing catastrophic failures.
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