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
The values of S and M_P (rounded-off to one decimal place) are
S = 2.0, M_P= 58.9 kN-m | |
S = 2.0, M_P=100.2 kN-m | |
S = 1.5, M_P= 58.9 kN-m | |
S = 1.5, M_P=100.2 kN-m |
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}
\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
The plastic moment, M_{p} calculated for the collapse mechanism using static method and kinematic method is
M_{P, \text { static }} \gt \frac{2 P L}{9}=M_{P, \text { kinematic }} | |
M_{P, \text { static }}=\frac{2 P L}{9} \neq M_{P, \text { kinematic }} | |
M_{P, \text { static }}=\frac{2 P L}{9}=M_{P, \text { kinematic }} | |
M_{P, \text { static }} \lt \frac{2 P L}{9}=M_{P, \text { kinematic }} |
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
aspect ratio | |
load factor | |
shape factor | |
slenderness ratio |
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
10.75 mm | |
12.25 mm | |
13.75 mm | |
15.25 mm |
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 ______
2 | |
4 | |
6 | |
8 |
Question 5 Explanation:
P_{u}=\frac{6M_{P}}{l} So, \alpha =6
There are 5 questions to complete.