Design Procedure

The design of Westok Cellular Beams is based on The Steel Deck Institute Publication 100 "Design of Composite and Non-Composite Cellular Beams", (referred to hereafter as P-100) modified as necessary to conform to the requirements of BS 5950-1:2000 and BS 5950:Part 3:Section 3.1:1990. Some further refinements in the design have been incorporated to conform to Westok's design approach.

Ultimate and Service limit state checks are carried out for composite beams at the construction stage and at the normal service stage. For non-composite beams, construction stage checks are not critical.

The following design checks are performed.

Shear on Gross Section

This is done by calculating the maximum shear along the span (this is usually one end or the other) from which the actual shear Fv is calculated and compared with the shear capacity Pv.

Shear on Net Section

This is done by calculating the maximum shear at the center of any cell and splitting the shear between the top and the bottom Tees, from which the design shear Fv is calculated and compared with the shear capacity Pv. The shear is divided between the top and bottom Tees in proportion to their shear areas. Each Tee is then independently checked for the applied shear apportioned to it.

Horizontal Shear (through web post)

This is done by calculating the worst horizontal shear, Fv, through any web post and comparing it with the shear capacity Pv. When the top piece is made from a different beam size than the bottom piece, the capacity is based on the thinner of the web thicknesses of the top and bottom pieces. As per BS 5950 Part 1:2000 for an unstiffened plate, the shear area is reduced by 10%. This check is performed for both the precomposite and postcomposite conditions for composite beams.

Web Post Buckling

This is done by calculating the capacity of the web post against a buckling failure, and comparing it to the actual factored forces on the most critical web post. This check is performed for both the precomposite and postcomposite conditions for composite beams.

The web post flexural and buckling capacity is checked for all web posts in the beam using the procedure outlined in SCI P-100, with some modification to conform to the methodology adopted by Westok.

Westok uses improved formulae which are valid for the range 1.3 < So/Do ≤ 1.8. This range is different from the range specified in the SCI P-100.

1.3 \leq \frac{S}{D_{o}} \leq 1.5

C_{1} = 6.874109 - 0.006589 \frac{D_{o}}{t} - 0.000050 {(\frac{D_{o}}{t})}^{2}

C_{2} = - 2.086963 - 0.005581 \frac{D_{o}}{t} + 0.000054 {(\frac{D_{o}}{t})}^{2}

C_{3} = - 4.759369 + 0.015300 \frac{D_{o}}{t} + 0.000036 {(\frac{D_{o}}{t})}^{2}

R F = C_{1} (\frac{S}{D_{o}}) + C_{2} {(\frac{S}{D_{o}})}^{2} + C_{3}

1.5 \leq \frac{S}{D_{o}} \leq 1.8

C_{1} = 65.465471 - 1.877093 \frac{D_{o}}{t} - 0.013142 {(\frac{D_{o}}{t})}^{2}

C_{2} = 19.273093 - 0.558715 \frac{D_{o}}{t} + 0.003940 {(\frac{D_{o}}{t})}^{2}

C_{3} = 55.673742 + 1.564808 \frac{D_{o}}{t} + 0.010854 {(\frac{D_{o}}{t})}^{2}

R F = {- C}_{1} (\frac{S}{D_{o}}) + C_{2} {(\frac{S}{D_{o}})}^{2} + C_{3}

Elastic moment capacity at the critical section:

M_{e} = Z_{e} p_{y} = {(S_{o} - 0.435 D_{o})}^{2} p_{y} t / 6

Moment capacity of post:

M_{c} = R F \times M_{e}

Maximum web post moment:

M_{h} = 0.9 R_{o} V_{h}

where

R_o

Radius of opening = D_o/2

Max unity factor = M_h/ M_c

Lateral Torsional Buckling / Unbraced Length

This check is done for Noncomposite Cellular Beams only. It is not done for Composite Cellular Beams since the deck continuously braces them, nor is it done for the precomposite condition. The bending capacity Mc is based on the gross cross section of the Cellular beam. The conditional limit state of Lateral Torsional Buckling is checked. For the calculation of the unbraced length, both the top and bottom flanges are considered to be braced wherever another beam or Cellular Beam frames in.

Vierendeel Bending

This check examines the combined effects of the bending and axial forces on the top and bottom Tees resulting from the shear and moments on the beam. The Vierendeel Bending check is performed on every Tee, at the top and bottom of the openings, and is performed for both the precomposite section and the composite section for composite Cellular Beams. The axial force and bending moment on the Tee is calculated at the center of each cell. The axial capacity Pc and the bending capacity Mc are based on the properties of the Tee. The interaction of the axial force and bending moment with the corresponding capacities is then calculated.