764in- k

Mu

= 23.6 - in3 < 26.0-in3 = ZW10x22 (386.7X103 mm3 < 426.1X103 mm3)

=

=

Z req 'd

F

Design longitudinal platform beams (see Figures J2-2, and J2-4);

P1u = (1/2)38.2k = 19.1k (89.96KN)

P2u = (1/2)P1u = 9.6k (42.70KN)

Therefore, reactions are; Ru = 19.1k (89.96KN)

The maximum moment occurs at mid span as;

Mu = [19.1k(5' 9.6k(2.5' ](12"/1' = 858in-k (96.95KN-m)

)

)

)

Figure J2-4. Loading on longitudinal beams

Note: Beam is laterally supported throughout its span

858in- k

Mu

= 26.5 - in3 > 26.0 = ZW10x22 (434.3X103 mm3 > 426.1X103 mm3)

Z req 'd =

=

F

(okay because of conservative assumptions)

Design columns;

Using load combination U = 1.4D;

Pu / column = 1.4(Wp1 + Wp2 )/# columns = 1.4(54.6k + 5k ) / 4 = 20.9 k /column (93.0KN/column)

Try W10x22;

Relevant properties of a W10x22 are as follows;

A = 6.49-in2 (4.19X103 mm2)

ry = 1.33-in (33.8mm)

rx = 4.27-in (108.5mm)

Check capacity of W10x22;

Note: Elements are in a braced frame with K = 1.0

Since KLy = KLx;

KL y 1.0(10' )(12"/1' )

=

= 90.2

ry

1.33"

From AISC LRFD Table 3-36;

(interpolated)

Design transverse beam to longitudinal beam connection (see Figures J2-2, and J2-5);

Use; Fy = 36ksi (248.2MPa), and Fu = 58ksi (399.9MPa)

Note: It was previously determined that the middle transverse beam supports half of Wp1 with the

distribution as shown in Figure J2-3. Therefore, the reaction can be taken as Ru = (1/2)38.2k = 19.1k

(89.96KN). One design will be made for this beam and used throughout for all transverse beam

connections. Formulas are taken from Part 9 of AISC LRFD volume II, 2nd edition.

Relevant properties of a W10x22 are as follows;

tw = 0.240-in (6.1mm)

bf = 5.750-in (146.1mm)

tf = 0.360-in (9.1mm)

d = 10.17-in (258.3mm)

Determine coping dimensions c and dc;

5.750"- 0.240"

c=

= 2.76 - in (70.1mm)

Say c = 3.0-in (76.2mm)

2

dc = 0.360" + 0.500" = 0.86" (21.8mm)

Say dc = 1.0-in (25.4mm)

Check flexural yielding of coped section assuming two 7/8-in. (22.2mm) φbolts;

Ru ≤ b n

where; φ= 0.9

e

Mn = FySnet

J2-4

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