Consider a beam whose cross$-$section is $496*500$:

$$ The outer concrete dimensions are the same

$$ The $8$ steel reinforcement bars are in the location, $1$ in each corners,$1$ in between the corners in each side with each diameter of $20$mm$.$

$$ The beam leng has a length L$,$ defined by the

span$/$depth ratio below $($the depth is the total concrete depth$).$

It is oriented such that the horizontal axis is the stiffer axis.

The vertical distance from the centre of the bar to top $($or bottom$)$ edge of the section, or the horizontal

distance from the centre of the bar to the side edge is called the cover. The depth of concrete cover

provides the fire performance and the durability resistance against steel corrosion which can cause spalling.

The beam can be considered as a simply supported beam of length L where L is based on the given span to

depth ratio of the beam. The beam experiences a vertically downwards point load P$,$ acting $0\mathrm{.}4$ L from the

left hand support, and also its own self weight.

You may assume that both materials exhibit linear elastic behaviour, with specific properties as given in the

table. Use Econc $=28000$ MPa and Esteel $=200000$ MPa; $\backslash$rho conc $=2400$ kg$/$m $3$ and $\backslash$rho steel $=7860$ kg$/$m$3.$ It is

sufficient to take gravity as g $=10$ m$/$s $2$

$.$

$1.$ What is the self mass and self weight of the beam per unit length?

$2.$ What value of P will cause the beam to crack due to tension in the concrete?

$3.$ Draw the stress and strain distribution $($with values$)$ for the cross$-$section where cracking first occurs

The engineer decides to move the location of the steel reinforcing bars by slightly decreasing the cover

dimensions $($ie moving the reinforcing bars closer to the outer edge$).$ The overall concrete dimensions do not

change.

$1.$ How are the strength and stiffness of the beam affected by the change.explain in few words. Diagrams are likely to improve the quality

of your answer.

f$($crack$)=4$ Mpa

span$/$depth $=19$