F. K. Kong MA, MSc, PhD, CEng, FICE, FIStructE, R. H. Evans CBE, DSc, D ès Sc, DTech, PhD, CEng, FICE, FIMechE, FIStructE (auth.)-Reinforced and Prestressed Concrete-Springer US (1987)

Unbraced frame analysis 423
loading on each of these is in proportion to its horizontal span. The
lateral loads given in Fig. 11.4-13 are so calculated.
The total lateral loading H is 10 kN and the sum of the spans is
26m; thus, in Fig. 11.4-13
Hl = H3 = 10 2~ 8 = 3.1 kN
H2 = 10 ~ lO = 3.8 kN
(Check: Hl + H2 + H3 = total lateral force H, i.e. 10 kN.)
The essence of the portal method is therefore
Hl - H!l_ H2 - H12 H3 13
and
- 'Ll - 'Ll 'Ll
Hl + H2 + H3 = H
By symmetry (Fig. 11.4-13),
Xl = 1Hl X2 = 1H2
By taking moments about points 5 and 6,
lVII = IV21 = ~ft~~~ = (~~)h = H;l
I (X2)h (H2)h h
IV2 I = IV31 = (/2)/2 = 12 = H'Ll
Therefore IV21 - IV2'1 = 0.
This means that the portal method implies that all the vertical
reaction due to the lateral loading is carried by the outside columns
only.
Taking moments for the complete roof frame about point 4,
Vl = 10 X 1.5/26 = 0.58 kN
and from above
HI (3·1) 5 H2 (3·81 6 H3 (3·1) 7
~I£. J: IE . J ~·~. ~l:±l
~ 11·55) ll·SS)t ~ 11·9) 11·9) t ~11·55) II·SS)t
I· .l118ml., 1- l2 110m) .I I. l3 (8ml .. l
VI V2 V2 1 V3 V3 1 V4
Fig. 11.4-13 Lateral loading for roof (kN)-portal method