Question $3$

A steel beam has a cross$-$section as shown in Figure $3.$ The allowable steel stresses are $\backslash (100\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$mm$\}2\backslash )($compression$)$ and $\backslash (150\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$mm$\}2\backslash )($tension$).$

a$)$ Determine the maximum moment that the beam can carry without failure and sketch the bending stress distribution for the maximum moment.

$[10$ marks$]$

b$)$ The shear force at a section of the beam is $\backslash (\backslash$mathrm$\{$F$\}=500\backslash$mathrm$\{$kN$\}\backslash )$ Calculate the maximum and minimum shear stresses in the web and sketch the shear stress distribution for the web.

$[15$ marks$]$

Fig. $3-$Shear Stress Question $2$

Analyze the beams shown in Figure $2$ using the Three$-$moment equation. Plot the bending moment and shear force diagrams.

$\backslash (\{\}^\{\backslash$mathrm$\{$ne$\}\}\backslash )$ marks$]$

$($a$)$

$($b$)$

Fig.