A $$450$$ $$mm$$ long plain concrete prism is subjected to the concentrated vertical loads as shown in the figure. Cross section of the prism is given as $$150\,\,mm\,\, \times \,\,150\,\,mm.$$ Considering linear stress distribution across the cross-section, the modulus of rupture (expressed in $$MPa$$) is ______________

For the stress state (in MPa) shown in the figure, the major principal stress is 10 MPa.

The shear stress $$\tau $$ is

An elastic isotropic body is in a hydrostatic state of stress as shown in the figure. For no change in the volume to occur, what should be its Poisson's ratio?

A fixed-end beam is subjected to a concentrated load $$(P)$$ as shown in the figure. The beam has two different segments having different plastic moment capacities $$\left( {{M_P},\,2{M_P}} \right)$$ as shown.

The minimum value of load $$(P)$$ at which the beam would collapse (ultimate load) is