First order design moments M

Consider grid C to determine Myyin column

Figure 5.7

Subframe on column C2 along grid C

Modified diagram required

Figure 5.7

Subframe on column C2 along grid C

According to BS EN 1991-1-1 6.3.1.2(11) the imposed load on the roof is category H and therefore does not qualify for reduction factor an.

Actions:

gk = (6.0 + 6.2) / 2 x 8.5 = 51.9 kN / m qk = (6.0 + 6.2) / 2 x 8.5 = 24.4 kN / m

Relative stiffness of lower column:

Assuming remote ends of slabs are pinned, relative stiffness

" blcdlc3/Llc + buAcXc + 0.75 b23d233/L23 + 0.75 b 21 d 21 3/L 21

where b = breadth d = depth L = length lc = lower column uc = upper column

2 x 0.54 / 4.5 + 0.75 x 6.1 x 0.33 / 8.6 + 0.75 x 6.1 x 0.33 / 9.6 = 0.0139 / (0.0278 + 0.0144 + 0.0129) = 0.252

1st order moment using Exp. (6.10)

FEM 23++ = 1.35 x 51.9 x 8.62 / 12 = 431.8 kNm FEM 21 = (1.35 x 51.9 + 1.5 x 24.4) x 9.62 / 12

= 106.7 x 9.62 / 12 = 819.5 kNm Mlower,yy = 0.252 x [819.5 - 431.8] = 97.7 kNm

1st order moment using Exp. (6.10a)

FEM 23 = 1.25 x 51.9 x 8.62 / 12 = 399.8 kNm FEM 21 = (1.25 x 51.9 + 1.5 x 24.4) x 9.62 / 12

= 101.5 x 9.62 / 12 = 779.5 kNm Mlower,yy = 0.252 x (779.5 - 399.8) = 95.7 kNm

1st order moment using Exp (6.10b)

FEM 23 = 1.35 x 51.9 x 8.62 / 12 = 431.8 kNm FEM 21 = (1.35 x 51.9 + 0.7 x 1.5 x 24.4 ) x 9.62 / 12

= 95.7 x 9.62 / 12 = 735.0 kNm Mlower,yy = 0.252 x (735.0 - 431.8) = 76.4 kNm

Consider grid 2 to determine Mj column.

300 thick ave 11470 wide gk= 97.5 kN/m /

-500sq

Figure 5.8

Subframe on column C2 along grid 2

4500

4500

Modified diagram required

Actions:

= 11.47 x 8.5 = 97.5 kN/m qk = 11.47 x 4.0 = 45.9 kN/m

Relative stiffness of lower column:

Assuming remote ends of slabs are fixed, relative stiffness

" 2 x 0.54 / 4.5 + 11.47 x 0.33 / 6.2 +11.47 x 0.33 / 6.0

1st order moment using Exp. (6.10)

= 200.5 x 6.22 / 12 = 642.3 kNm FEM CD = 1.35 x 97.5 x 6.02 / 12 = 394.9 kNm Mlowe,22 = 0.107 x (642.3 - 394.9) = 26.5 kNm

1st order moment using Exp. (6.10a)

FEM CB = 1.25 x 97.5 x 6.02 / 12 = 365.6 kNm FEM CD = (1.25 x 97.5 + 1.5 x 45.9) x 6.22 / 12

= 190.7 x 6.22 / 12 = 611.0 kNm Mlowe,zz = 0.107 x (611.0 - 365.6) = 26.3 kNm

1st order moment using Exp. (6.10b)

FEM CB = (1.35 x 97.5 + 0.7 x 1.5 x 45.9) x 6.22 / 12

= 190.7 x 6.22 / 12 = 576.0 kNm FEM CD = 1.35 x 97.5 x 6.02 / 12 = 394.9 kNm Mlower,zz = 0.107 x (576.0 - 394.9) = 19.4 kNm

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