Question $2$: $[75$ Marks$]$

$101$

a$)$ For the portal frame shown in Figure Q$2,E=210$GPa, both the columns and the beam have $I=23\mathrm{.}1{10}^{6}m{m}^4.$

i$.$ Determine the bending moment diagram using the slope deflection method, showing all salient points $($i$.$e$.$ maximum moments, points of inflexion etc.

$[25$ marks$]$

ii$.$ Determine the bending moment diagram using the flexibility method and calculate the horizontal deflection of point B;

$[35$ marks$]$

b$)$ Determine the bending moment diagram using any suitable structural software, and compare the results with the above solutions. Comment on the differences, if any, with answers obtained from $($a$)$ above. Attach the computer printout of the bending moment diagram only as part of your report.

$[10$ marks$]$

c$)$ Determine the horizontal deflection at point B using any suitable structural software. Comment on the differences, if any, with the results obtained in $($a$)$ above. Attach the computer printout of deflections only as part of your report.

$[5]$ marks$]$