Plastic Analysis


Question 1
For the square steel beam cross-section shown in the figure, the shape factor about z- z axis is S and the plastic moment capacity is M_P. Consider yield stress f_y = 250 MPa and a = 100 mm.

The values of S and M_P (rounded-off to one decimal place) are
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
GATE CE 2022 SET-2   Design of Steel Structures
Question 1 Explanation: 
Shape factor for diamond shaped section = 2
\begin{aligned} S&=\frac{M_P}{M_y}=\frac{f_yZ_P}{f_yZ_e}\\ M_P&=S.M_y=S.f_y.Z_e \end{aligned}


\begin{aligned} I_{ZZ}&=\frac{a^4}{12}\\ Z_{ZZ}&=\frac{a^4 \times \sqrt{2}}{12 \times a }=\frac{\sqrt{2}a^3}{12}mm^3\\ M_P&=\left [ 2 \times 250 \times \frac{\sqrt{2} \times (100)^3}{12} \right ] \times 10^{-6} kNm\\ &=58.93kNm \end{aligned}
Question 2
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
A
M_{P, \text { static }} \gt \frac{2 P L}{9}=M_{P, \text { kinematic }}
B
M_{P, \text { static }}=\frac{2 P L}{9} \neq M_{P, \text { kinematic }}
C
M_{P, \text { static }}=\frac{2 P L}{9}=M_{P, \text { kinematic }}
D
M_{P, \text { static }} \lt \frac{2 P L}{9}=M_{P, \text { kinematic }}
GATE CE 2021 SET-2   Design of Steel Structures
Question 2 Explanation: 


\begin{aligned} \text{At collapse,} \quad M_{p} \theta+M_{p} \phi&=P \Delta\\ \Rightarrow \quad \quad 3 M_{P} \frac{\Delta}{l}+\frac{3 M_{P} \Delta}{2 l} &=P \Delta \\ M_{P} &=\frac{2 P l}{9}\\ \text{Also,} \qquad\qquad \quad M_{P ,\text { static }}&=M_{P,\text{ kinematic}} \end{aligned}


Question 3
The ratio of the plastic moment capacity of a beam section to its yield moment capacity is termed as
A
aspect ratio
B
load factor
C
shape factor
D
slenderness ratio
GATE CE 2020 SET-2   Design of Steel Structures
Question 3 Explanation: 
Ratio of \frac{M_p}{M_y}= Shape factor
Question 4
If the section shown in the figure turns from fully-elastic to fully-plastic, the depth of neutral axis (N.A.), \bar{y}, decreases by
A
10.75 mm
B
12.25 mm
C
13.75 mm
D
15.25 mm
GATE CE 2019 SET-1   Design of Steel Structures
Question 4 Explanation: 


\bar{y}=\frac{A_1y_1+A_2y_2}{A_1+A_2}=\frac{300\times 2.5+300 \times 35}{300+300}=18.75m

Question 5
A prismatic propped cantilever beam of span L and plastic moment capacity M_{p} is subjected to a concentrated load at its mid-span. If the collapse load of the beam is \alpha \frac{M_{p}}{L}, the value of \alpha is ______
A
2
B
4
C
6
D
8
GATE CE 2018 SET-2   Design of Steel Structures
Question 5 Explanation: 



P_{u}=\frac{6M_{P}}{l} So, \alpha =6


There are 5 questions to complete.

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