PART $2$: SYSTEM STIFFNESS CHECKS

In this part we will undertake design checks in relation to the lateral stiffness of the portal frame

system. To help with this, note that for a portal frame structure with pinned base supports, the lateral

displacement, $D_f,$ due to a lateral wind load, W $,$ acting at the top of the columns, can be

approximated $($from Silva and Badie $2008)$ as:

${}_f=(4+\frac{2L_b{I}_c}{L_c{I}_b})\frac{W{L}_c^3}{24E{I}_c}$

where $L_b$ and $L_c$ are shown in Figure $7($conservatively use the maximum $L_c$ value$),l_b$ and $I_c$ are the

second moment of inertia of the beams and columns respectively and $E$ is the material modulus of

elasticity.

Figure $7.$ Illustrating the deformed shape of a portal frame structure subject to a roof$-$level lateral load W$.$

Q$3.$ If you are to design the portal frame for an SLS wind lateral load of $W=10kN($per portal frame$),$

what is the lightest UB steel section size would you require in order to limit the lateral drift of the

building $($lateral displacement at top of columns divided by the column height$)$ to H$/200?$ Note that

you can assume that the same steel UB section will be used for both the columns and beams $($i$.$e$.$

$I_b=I_c).$ Also note that the back of the course reader provides tables with section properties for size

different steel sections. Report the UB section size, e$.$g$.610$UB$125$

Answer: