A $$12$$ $$mm$$ bracket plate is connected to a column flange as shown in the figure below. The bracket transmits a load of $$W = 200\,\,kN$$ to the column flange. $$A$$ $$10$$ $$mm$$ fillet weld is provided along $$AB,$$ $$BC$$ and $$CD.$$ If $$e=350$$ $$mm,$$ $$b=200$$ $$mm$$ and $$d=600$$ $$mm,$$ Verify if the size of the weld provided is adequate. Allowable shearing stress in the fillet weld can be taken to be $$108$$ $$MPa.$$

A two span beam with an internal hinge is shown below.

Conjugate beam corresponding to this beam is

For the structure shown below, the vertical deflection at point $$A$$ is given by

A frame $$ABCD$$ is supported by a roller at $$A$$ and is on a hinge at $$C$$ as shown below:

The reaction at the roller end $$A$$ is given by