A continuous beam $$250\,mm \times 450\,mm$$ carries $$6$$ numbers of $$12$$ $$mm$$ diameter longitudinal bars as shown. The factored shear force at the point of inflection is $$200$$ $$kN.$$ Check if the beam is safe in bond. Assume $$M15$$ mix with $${\sigma _{ck}} = 15\,\,N/m{m^2}$$ and mild steel with $${\sigma _y} = 250\,N/m{m^2}.$$ A clear cover of $$25$$ $$mm$$ can be assumed. The design bond stress for mild steel bars in $$M15$$ concrete is specified to be $$1.0\,N/m{m^2}.$$

A simply supported rectangular prestressed concrete beam $$200$$ $$mm$$ wide and $$400$$ $$mm$$ deep has an effective span of $$12$$ $$m.$$ The prestressing cable has a triangular profile with zero eccentricity at ends and $$70$$ $$mm$$ at the midspan as shown in the figure below. The effective prestress is $$800$$ $$kN$$ after all losses. Determine the value of point load, the beam can support at the midspan if the pressure line passes through the upper kern of the section. The weight density of the material of the beam can be taken to be $$25$$ $$kN/{m^3}$$

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