The portal frame shown in the figure is subjected to a uniformly distributed vertical load $$w$$ (per unit length).

The bending moment in the beam at the joint $$'Q'$$ is

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

A motorist traveling at 100 km/h on a highway needs to take the next exit, which has a speed limit of 50 km/h. The section of the roadway before the ramp entry has a downgrade of 3% and coefficient of friction ( f ) is 0.35. In order to enter the ramp at the maximum allowable speed limit, the braking distance (expressed in m) from the exit ramp is ______