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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
$$\eqalign{ & At\,\,the\,\,end\,\,'A'\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,At\,\,the\,\,end\,\,'B' \cr & \,\,\,\,\,\,\,\,\,{{3EI\Delta } \over {{\ell ^2}}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0 \cr} $$
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