Real Life Applications:
This method is also known as method of load factor design or ultimate load design. The strength of steel beyond the yield stress is fully utilized in this method. This method also provides striking economy as regards the weight of steel since the sections designed by this method are smaller in size than those designed by the method of elastic design. Plastic design method has its main application in the analysis and design of statically indeterminate framed structures.
The main difference between elastic and plastic deign is the assumption of the behavior of the structure. In elastic design we assume that structure will fail if it reaches elastic limit but in plastic analysis we consider that structure will fail when it reaches lower yield point.
In plastic design we have to consider the deformed shape of the structure and analyze the secondary loads developed due to the deformation. Here we also discuss about the Shape Factors (S= Plastic Moment/ Yield Moment)
for different type of sections like it can be different for rectangular section, I-Section, Circular Section etc. The fundamental conditions of plastic analysis are
a) Equilibrium Condition:
b) Yield Condition: At collapse, bending moment at any section should not exceed the plastic moment capacity of the beam cross- section. (Mp
c) Mechanism Condition: At the collapse condition, sufficient no of plastic hinges must be developed so that a part or entire structure must transform into a mechanism, leading to collapse.
Theorem of Plastic Analysis:
A) Static Theorem (Lower Bound Theorem)
Static Theorem satisfies equilibrium and yield conditions. It states that the collapse load found on the basis of collapse B.M.D (in which B.M at any section is less than or equal to Mp
) will always be less than or equal to collapse load. (P£ Pu
). Static method represents the lower limit of true ultimate load and has maximum factor of safety.
B) Kinematic Theorem (Upper Bound Theorem):
Here equilibrium and mechanism conditions are satisfied. It states that the collapse load found by assuming the mechanism will always be greater than or equal to the collapse load (P³ Pu
Where, P= Calculated collapse load,
= True collapse load.