1
GATE CE 1991
MCQ (Single Correct Answer)
+1
-0.3
The moments at the end $$'A'$$ and $$'B'$$ of a beam $$'AB'$$ where end $$(a)$$ is fixed and $$(b)$$ is hinged, when the end $$(b)$$ sinks by an amount $$\Delta $$ are given as
A
$$\eqalign{ & At\,\,the\,\,end\,\,'A'\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,At\,\,the\,\,end\,\,'B' \cr & \,\,\,\,\,\,\,\,\,{{6EI\Delta } \over {{\ell ^2}}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{6EI{\rm A}} \over {{\ell ^2}}} \cr} $$
B
$$\eqalign{ & At\,\,the\,\,end\,\,'A'\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,At\,\,the\,\,end\,\,'B' \cr & \,\,\,\,\,\,\,\,\,{{6EI\Delta } \over {{\ell ^2}}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0 \cr} $$
C
$$\eqalign{ & At\,\,the\,\,end\,\,'A'\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,At\,\,the\,\,end\,\,'B' \cr & \,\,\,\,\,\,\,\,\,{{3EI\Delta } \over {{\ell ^2}}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{3EI\Delta } \over {{\ell ^2}}} \cr} $$
D
$$\eqalign{ & At\,\,the\,\,end\,\,'A'\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,At\,\,the\,\,end\,\,'B' \cr & \,\,\,\,\,\,\,\,\,{{3EI\Delta } \over {{\ell ^2}}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0 \cr} $$
2
GATE CE 1991
MCQ (Single Correct Answer)
+1
-0.3
For a given shear force across a symmetrical $$'{\rm I}'$$ section the intensity of shear stress is maximum at the
A
Extreme fibres
B
Centroid of the section
C
At the junction of the flange and the web, but on the web
D
At the junction of the flange and the web, but on the flange.
3
GATE CE 1991
MCQ (Single Correct Answer)
+1
-0.3
A thin cylindrical vessel of mean diameter $$D$$ and of length $$'L'$$ closed at both the ends is subjected to a water pressure $$'P'$$. The value of hoop stress and longitudinal stress in the shell shall be respectively.
A
$${{PD} \over {2t}}.{{PD} \over {4t}}$$
B
$${{PD} \over {8t}}.{{PD} \over {8t}}$$
C
$${{PD} \over {4t}}.{{PD} \over {8t}}$$
D
$${{PD} \over t}.{{PD} \over {2t}}$$
4
GATE CE 1991
MCQ (Single Correct Answer)
+1
-0.3
A cantilever beam of tubular section consists of 2 materials copper as outer cylinder and steel as inner cylinder. It is subjected to a temperature rise of $$20^\circ C$$ and $$\alpha_{copper}\;>\;\alpha_{steel}$$ the stresses developed in the tubes will be
A
compression in steel and tension in copper.
B
compression in copper and tension in steel.
C
No stress in both.
D
Tension in both the materials.