1

GATE CE 2002

A steel beam (with a constant $EI,$ and span $L$) is fixed at both ends and carries a uniformly distributed load ($w$ $kN/m$), which is gradually increased till the beam reaches the stage of plastic collapse (refer to the following figure). Assuming $'B'$ to be at mid-span, which of the following is true.
A
Hinges are formed at $A,B$ and $C$ together
B
Hinges are formed at $B$ and then at $A$ and $C$ together
C
Hinges are formed at $A$ and $C$ together and then at $B$
D
Hinges are formed at $A$ and $C$ only
2

GATE CE 2000

The four cross sections shown below are required to be ordered in the increasing order of their respective shape factors.
A
${\rm I}{\rm I}{\rm I},\,\,{\rm I},\,\,{\rm I}V,{\rm I}{\rm I}$
B
${\rm I},\,\,{\rm I}{\rm I},\,\,{\rm I}{\rm I}{\rm I},{\rm I}V$
C
${\rm I}{\rm I}{\rm I},\,\,{\rm I}V,\,\,{\rm I},\,\,{\rm I}{\rm I}$
D
${\rm I}{\rm I}{\rm I},\,\,{\rm I}V,\,\,{\rm I}{\rm I},\,\,{\rm I}$
3

GATE CE 2000

A cantilever beam of length $L$ and a cross section with shape factor $'f'$ supports a concentrated load $P$ as shown below:

The length ${L_P}$ of the plastic zone, when the maximum bending moment, equals the plastic moment ${M_P}$, given by

A
${{{L_P}} \over L} = {1 \over f}$
B
${{{L_P}} \over L} = L\left( {1 - f} \right)$
C
${{{L_P}} \over L} = 1 - {1 \over {\sqrt f }}$
D
${{{L_P}} \over L} = 1 - {1 \over f}$
4

GATE CE 1999

The shape factor of the section shown in fig. is
A
$1.5$
B
$1.12$
C
$2$
D
$1.7$