Task $1$

$($This task relates to a section of bar found in the stores which may be used in the

construction of a bridge over a culvert on the test$-$track$)$

A simply supported beam of effective length $10$ m and section dimensions $80$ mm by

$40$ mm $,$ is subjected to the following loading system: a full$-$length UDL of $80$ N per metre

of length and a point load of $200$ N at a distance of $4$ m from the left$-$hand end.

Calculate the support forces at each end.

Produce a shear force diagram.

Produce a bending moment diagram.

From the bending moment diagram, calculate the maximum bending stress.

If the beam material has a mass of $4$ kg per metre length, sketch a new bending

moment diagram to take this into account and calculate the new

maximum bending stress.

Task $2$

$($i$)($An inspection pit in a workshop requires a beam over it for hoisting purposes $-$ the

task involves determining which $($if any$)$ of some available beams are suitable.$)$

A simply supported I $-$section beam of effective length $3$ m has a $6$ kN point load acting at

its mid$-$point. The beam is required to have a maximum bending stress of $1\mathrm{.}4$ MPa $.$

There are three $3$ m spans available:

$610$ xx$305$ xx$238$

$762$ xx$267$ xx$147$

$838$ xx$292$ xx$176$

Choose the most appropriate beam and justify your decision.

$($ii$)$ A hot$-$finished circular$-$section steel column is to be used in an application as part of a

vehicle inspection platform in which the axial end load is applied compressively but

offset from the centroid. The offset is to be $50$ mm and must not cause the stress to be

tensile at any part of the section. There are four choices of column available.

Choose the most appropriate column and justify your selection,