Plastic Analysis Civil Engineering (CE) Notes | EduRev

Q.1 If the section shown in figure turns from fully elastic to fully plastic, the depth of neutral axis (NA), decreases by    [2019 : 2 Marks, Set-I]

(a) 12.25 mm
(b) 15.25 mm
(c) 10.75 mm
(d) 13.75 mm
Ans. (D)
Solution:


= 46.25 mm
NA - Neutral axis
The section is unsymmetrical about the NA and hence the equal area axis (EA) has to be located




Q.2  The dimension of a symmetrical welded l-section are shown in the figure.
   
The plastic section modulus about the weaker axis (in cm³, up to one decimal place) is _____.    [2018 : 2 Marks, Set-I]
Solution:


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  (M_P, 2M_p) as shown.

The minimum value of load (P) at which the beam would collapse (ultimate load is)     [2016 : 2 Marks, Set-II]




Ans. (A)
Solution:
D_s = 2
∴ Number of plastic hinge required for complete collapse = D_s + 1
= 2 + 1 = 3
Mechanism 1:


⇒
For principal of virtual work done,


Mechanism 2:



Q.4   A fixed end beam is subjected to a load, W at 1 /3^rd span from the left support as shown in the figure. The collapse load of the beam is    [2015 : 2 Marks, Set-II]

(a) 16.5 M_p/L
(b) 15.5 M_p/L
(c) 15.0 M_p/L
(d) 16.0 M_p/L
Ans. (C)
Solution:
No. of plastic hinges formed at collapse
= r + 1 = 3
There can be two collapse mechanisms
Case (I)


⇒ θ = 2α
Internal work done = External work done



Case (II)



Hence, minimum collapse load is 15M_p/L.

Q.5  For formation of collapse mechanism in the following figure, the minimum value of P_u is  M_p and 3M_p denote the plastic moment capacities of beam sections as shown in this figure. The value of c is ____.    [2015 : 2 Marks, Set-I]

Solution:
As L is not defined in question. So, by assuming L = 1 m
Mechanism 1:

Mechanism 2:


Failure load obtained out of two mechanisms
 
∴

Q.6 A prismatic beam (as shown below) has plastic moment capacity of M , then the collapse load M_P of the beam is    [2014 : 2 Marks, Set-II]





Ans. (C)
Solution:
Here degree of static indeterminacy = 0
∴ Number of plastic hinges required for mechanical equlibrium
= D_s + 1 = 0 + 1 = 1
Mechanism 1:

From principal of virtual work

Mechanism 2:

From principal of virtual work, equating external work donw to internal work done


∴

Q.7  The ultimate collapse load (P) in terms of plastic moment M_p 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]





Ans. (C)
Solution:

From principal of virtual work


Q.8   A propped cantilever made of a prismatic steel beam is subjected to a concentrated load P at mid span as shown.

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:



Q.9  A propped cantilever made of a prismatic steel beam is subjected to a concentrated load P at mid span as shown.

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



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.