QUESTION $1-100$ marks

A concrete floor slab is built integrally with a beam so that $\text{'}T\text{'}$ action can be considered

as shown in the cross section from figure $2.$ The beam is part of a frame in a multi$-$storey building. The bending moment diagram from two ultimate limit state loading

conditions between the column faces is also shown below $($in Figure $1).$

$($a$)$ Determine the top and bottom reinforcement for the beam presented in the

next figures. Check for maximum and minimum steel. Bar spacing is the

smaller of $25mm$ or bar diameter. Do not use bars greater than $30mm.$

$73$ marks

$($b$)$ Calculate the maximum design shear force at the column face that can be

resisted by $3$ legged R$10$ stirrups at $150mm$ centres.

$($c$)$ Sketch cross sections of the beam at the mid$-$span and column face.

$6$ marks

Assume for:

$-$concrete: specified compressive strength$=40$ MPa; cover $=30mm$; maximum concrete strain $=0\mathrm{.}003$

$-$ steel: main bars $=$ Grade $500$; stirrups $=$ Grade $300$; modulus elasticity $=200$GPa

Fig $1-$ Bending Moment Diagram $($kNm$)$

Fig $2-$ Beam section