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Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)

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Q.1 If the section shown in figure turns from fully elastic to fully plastic, the depth of neutral axis (NA),Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE) decreases by    [2019 : 2 Marks, Set-I]
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
(a) 12.25 mm
(b) 15.25 mm
(c) 10.75 mm
(d) 13.75 mm
Ans.
(D)
Solution:
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
= 46.25 mm
NA - Neutral axis
The section is unsymmetrical about the NA and hence the equal area axis (EA) has to be located
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)

Q.2  The dimension of a symmetrical welded l-section are shown in the figure.
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)   
The plastic section modulus about the weaker axis (in cm3, up to one decimal place) is _____.    [2018 : 2 Marks, Set-I]
Solution:

Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Note: Keep in wind the units and decimal places.

Q.3 A fixed-end beam is subjected to a concentrated load (P) as shown in the figure. The beam has two different segments having different plastic moment capacities  (MP, 2Mp) as shown.
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
The minimum value of load (P) at which the beam would collapse (ultimate load is)     [2016 : 2 Marks, Set-II]
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Ans.
(A)
Solution:
Ds = 2
∴ Number of plastic hinge required for complete collapse = Ds + 1
= 2 + 1 = 3
Mechanism 1:
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
For principal of virtual work done,
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Mechanism 2:
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)

Q.4   A fixed end beam is subjected to a load, W at 1 /3rd span from the left support as shown in the figure. The collapse load of the beam is    [2015 : 2 Marks, Set-II]
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
(a) 16.5 Mp/L
(b) 15.5 Mp/L
(c) 15.0 Mp/L
(d) 16.0 Mp/L
Ans.
(C)
Solution:
No. of plastic hinges formed at collapse
= r + 1 = 3
There can be two collapse mechanisms
Case (I)
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
⇒ θ = 2α
Internal work done = External work done
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Case (II)
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Hence, minimum collapse load is 15Mp/L.

Q.5  For formation of collapse mechanism in the following figure, the minimum value of Pu is Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE) Mp and 3Mp denote the plastic moment capacities of beam sections as shown in this figure. The value of c is ____.    [2015 : 2 Marks, Set-I]
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Solution:
As L is not defined in question. So, by assuming L = 1 m
Mechanism 1:
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Mechanism 2:
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Failure load obtained out of two mechanisms
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE) 
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)

Q.6 A prismatic beam (as shown below) has plastic moment capacity of M , then the collapse load MP of the beam is    [2014 : 2 Marks, Set-II]
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Ans. 
(C)
Solution:
Here degree of static indeterminacy = 0
∴ Number of plastic hinges required for mechanical equlibrium
= Ds + 1 = 0 + 1 = 1
Mechanism 1:
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
From principal of virtual work
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Mechanism 2:
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
From principal of virtual work, equating external work donw to internal work done
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)

Q.7  The ultimate collapse load (P) in terms of plastic moment Mp by kinematic approach for a propped cantilever of length L with Pacting at its mid-span as shown in the figure, would be    [2014 : 1 Mark, Set-I]
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Ans.
(C)
Solution:
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
From principal of virtual work
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)

Q.8   A propped cantilever made of a prismatic steel beam is subjected to a concentrated load P at mid span as shown.
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)

If the magnitude of load Pis increased till collapse and the plastic moment carrying capacity of steel beam section is 90 kNm, determine reaction R (in kN) (correct to 1-decimal place) using plastic analysis ________.    [2013 : 2 Marks]
Solution:

Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)

Q.9  A propped cantilever made of a prismatic steel beam is subjected to a concentrated load P at mid span as shown.
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
If load P = 80 kN, find the reaction R (in kN) (correct to 1 decimal place) using elastic analysis______.    [2013 : 2 Marks]
Solution:

Equating deflection at end B,
Let, l = 3 m
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)
Past Year Questions: Plastic Analysis Notes | Study Design of Steel Structures - Civil Engineering (CE)

Q.10  As per IS 800 : 2007 the cross-section in which extreme fibre can reach the yield stress but can not develop the plastic moment of resistance due to local buckling is classified as    [2013 : 1 Mark]
(a) plastic section
(b) compact section
(c) semi compact section
(d) shear section
Ans. 
(C)
Solution:
Plastic section: Cross-section which can develop plastic hinges and have the rotation capacity required for the failure of the structure by formation of plastic mechanism.
Compact section: Cross-section which can develop plastic moment of resistance but have inadequate plastic hinge rotation capacity for formation of plastic mechanism before buckling.
Semi compact: Cross-sections, in which the expense fibre in compression can reach yield stress, but cannot develop plastic moment of resistance due to location buckling.
Slender: Cross-sections in which the elements buckle locally even before attainment of yield stress are closed as sledner sections.

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