Past Year Questions: Plastic Analysis | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE) PDF Download

Q1: The steel angle section shown in the figure has elastic section modulus of 150.92 cm³ about the horizontal X-X axis, which passes through the centroid of the section.
The shape factor of the section is_______ (rounded off to 2 decimal places) [GATE CE 2024 SET-2]
Ans: 1.75 to 1.85
Shape factor = Z_p/Z_e

SF = 270/150.92 = 1.79

Q1: For the square steel beam cross-section shown in the figure, the shape factor about z − z axis is SS and the plastic moment capacity is M_P. Consider yield stress f_y = 250 MPa and a = 100mm.  The values of S and M_P (rounded-off to one decimal place) are [GATE CE 2022 SET-2]
(a) S = 2.0, M_P = 58.9 kN−m
(b) S = 2.0, M_P = 100.2 kN−m
(c) S = 1.5, M_P = 58.9 kN−m
(d) S = 1.5, M_P = 100.2 kN−m
Ans: (a)
Shape factor for diamond shaped section = 2

I_ZZ = a⁴/12

= 58.93 kNm

Q1: A prismatic steel beam is shown in the figure.
The plastic moment, M_p calculated for the collapse mechanism using static method and kinematic method is [GATE CE 2021 SET-2]
(a) M_P, _static > 2PL/9 = M_P, _kinematic 
(b) M_P, _static = 2PL/9 M_P, _kinematic
(c) M_P, _static = 2PL/9 = M_P, _kinematic
(d) M_{P, static} < 2PL/9 = MP, kinematic 
Ans: (c) 

At collapse, M_pθ + M_pϕ = PΔ
⇒

M_p = 2Pl/9
Also, M_P, _static = M_P, _kinematic

Q1: The ratio of the plastic moment capacity of a beam section to its yield moment capacity is termed as   [GATE CE 2020 SET-2]
(a) aspect ratio
(b) load factor
(c) shape factor
(d) slenderness ratio
Ans: (c)
Ratio of M_p/M_y = Shape factor

Q1: 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)

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

Q1: 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]
Ans:

Note: Keep in wind the units and decimal places.

Q1: 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)
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:

Q1:   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)
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.

Q2:  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]

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

Mechanism 2:


Failure load obtained out of two mechanisms

∴

Q1: 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)
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

∴

Q2: 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)

From principal of virtual work

Q1: 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]
Ans:

Q2:  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]
Ans: Equating deflection at end B,
Let, l = 3 m

Q3:  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)
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.