Diaphragm effect - stressed skin design
To introduce the concept of stressed skin design and to discuss the practical applications of this method.
RELATED WORKED EXAMPLES
Worked example 9.1: Stressed skin design
This lecture explains the contribution that profiled sheets of roofing, flooring, and walls make to the resistance and stiffness of frameworks by virtue of their resistance and stiffness in shear (shear diaphragms). Procedures and tables for the calculation of the resistance and flexibility of diaphragms are given. The practical applications of stressed skin design are also discussed.
a = length of diaphragm in a direction perpendicular to the corrugations (mm)
A = cross-section area of longitudinal edge member (mm2)
b = depth of diaphragm in a direction parallel to the corrugations (mm)
c = overall shear flexibility of a diaphragm (mm/kN)
d = pitch of corrugations (mm)
E = modulus of elasticity of steel (210 kN/mm2 - 210 000MPa)
fy = yield strength of steel in sheeting (kN/mm2)
Fp = design shear resistance of individual sheet/purlin fastener (kN) (see Table1)
Fs = design shear resistance of individual seam fastener (kN) (see Table 1)
Fsc = design shear resistance of individual sheet/shear connector fastener (kN) (see Table 1)
h = height of profile (mm)
k = frame flexibility (mm/kN)
K = sheeting constant (see Tables 4 and 5)
l = width of corrugation crest (mm)
L = span of diaphragm between braced frames (mm)
n = number of panels in the length of the diaphragm assembly
nb = number of sheet lengths within depth of diaphragm
nf = number of sheet/purlin fasteners per sheet width
np = number of purlins (edge + intermediate)
ns = number of seam fasteners per side lap (excluding those which pass through both sheets and the supporting purlin)
nsc = number of sheet/shear connector fasteners per end rafter
n1sc = number of sheet/shear connector fasteners per intermediate rafter
nsh = number of sheet widths per panel
p = pitch of sheet/purlin fasteners (mm)
q = distributed shear load on diaphragm (kN/mm)
sp = slip per sheet/purlin fastener per unit load (mm/kN) (see Table1)
ss = slip per seam fastener per unit load (mm/kN) (see Table1)
ssc = slip per sheet/shear connector fastener per unit load (mm/kN) (see Table1)
t = net sheet thickness, excluding galvanising and coating (mm)
V = applied shear force on diaphragm (kN)
V* = design shear resistance of diaphragm (kN)
Vcr = shear force on diaphragm to cause overall shear buckling (kN)
VR = resistance associated with a given failure mode or ultimate load (kN)
α1, α2, α3 = factors to allow for intermediate purlins (see Table 3)
α4 = factor to allow for number of sheet lengths
For the case considered, a4 = (1 + 0.3nb)
ß1,ß2 = factors to allow for the number of sheet/purlin fasteners per sheet width (see Table 2)
ß3 = distance between outermost fasteners across the sheet width divided by sheet width
For sheeting (seam fasteners in the crests) ß3 =
For decking (seam fasteners in the troughs) ß3 = 1.0
Δ = midspan deflection of a panel assembly (mm)
υ = Poisson's ratio for steel (0.3)
1. INTRODUCTION - DESIGN PRINCIPLES
1.1 Diaphragm action
It has long been recognised that a building framework is considerably strengthened and stiffened once the roof, floors, and walls have been added. Frame stresses and deflections calculated on the basis of the bare frame are usually quite different from the real values. By taking the cladding into account, the actual behaviour of the building can be predicted and, usually, worthwhile savings may be made in the costs of the frames.
The contribution that profiled sheets of roofing, flooring, and side cladding make to the resistance and stiffness of frameworks is by virtue of their resistance and stiffness in shear, i.e. the resistance of rectangular panels to being deformed into parallelograms. Known as the 'diaphragm effect' in literature, such panels are, hence, known as 'shear diaphragms' or simply 'diaphragms.' In the United States, the design method which takes this effect into account is called 'diaphragm design,' whereas in Europe it is called 'stressed skin design.'
Profiled steel sheeting used as roof sheeting or decking, floor decking, or side cladding is very effective as a shear diaphragm. Provided it is positively attached to the secondary members and main frames by mechanical fasteners or welding, it is extremely reliable and predictable and may be confidently used as a structural component. Moreover, it has been verified by many full scale tests and proven by practical experience of many buildings designed on this basis.
The principles of stressed skin design may be illustrated with reference to flat-roofed or pitched-roof buildings. In a flat-roofed building subjected to side load (see Figure 1), each of the roof panels acts as a diaphragm taking load back to the gable ends which are stiffened in their own planes by bracing or sheeting.
In a pitched-roof building (see Figure 2) under vertical or side load, there is a component of load down the roof slope so that the roof diaphragms tend to prevent the building from spreading or swaying. The flatter the roof pitch, the less effective the diaphragms are in resisting vertical load, but the more effective they are in resisting horizontal load.
The sheeting in Figures 1 and 2 acts in the roof such that the roof behaves like a deep plate girder. Under in-plane load, the end gables take the reactions, the sheeting acts as a web and takes the shear, and the edge members act as flanges and take the axial tension and compression. In no case does the sheeting help the frames to resist bending out of the plane of the sheeting.
1.2 Suitable forms of construction
If the frames of Figure 1 are pin-jointed, then the horizontal loads are resisted entirely by stressed skin action. In this case, the structure must be adequately braced during erection and the sheeting panels must not be removed without proper consideration.
If the frames of Figure 1 have rigid joints, then the horizontal loads are shared between the frames and the diaphragms. In this case, it is good practice for the frames alone to be designed to carry the full characteristic load without collapse and for the completed stressed skin building to be designed to carry the full design load. The diaphragms then effectively provide the required load factor.
Stressed skin design should be used predominantly in low-rise buildings where the roof and floors can behave as a deep plate girder, as shown in Figure 1.
It should be noted that diaphragm action will always occur during the real life of building, whether or not it is taken into account in design and calculation. Therefore, tested and measured performances of profiled sheets should be different if they are considered suitable, partially suitable, or unsuitable for diaphragm actions.
1.3 Benefits, conditions, and restrictions
Some of the benefits of stressed skin design are as follows:
a. Calculated frame stresses and deflections are usually much less than in the bare frame.
b. Calculated and observed stresses and deflections agree, so the design is more realistic.
c. Bracing in the plane of the roof is eliminated or frame sizes are reduced.
d. Frame details are standardised.
e. Contribution of profiled sheets to seismic resistance could be particularly effective, limiting the need to increase the weight of the steel structure.The method is particularly effective where lateral loads act only on one or two frames, e.g. cross surge from light overhead cranes.
f. The method is particularly effective where lateral loads act only on one or two frames, e.g. cross surge from light overhead cranes.
g. By taking diaphragm action into account the actual forces on the cladding and fasteners can be calculated.
In order for steel sheeting to act as a diaphragm, the following conditions must be met:
a. End gables must be braced or sheeted.
b. Edge members must be provided to panels, and these members and their connections must be designed to carry the flange forces.
c. Sheeting must be fastened to members with positive connections, such as self drilling screws, cartridge fired pins, or welding.
d. Seams between sheets must be fastened with positive connections.
e. Suitable structural connections must be provided to transmit diaphragm forces into the main framework.
f. Profiled sheets dimensional tolerances should be positive (0, +X) in order to always be on the safe side.
g. It is recommended that the shear stress in the sheets be less than 25% of the ordinary bending stress in the sheets, so that if the sheets are corroded, they will fail in bending long before the stressed skin building is endangered.
h. It is recommended that roof light openings should be less than 3% of the relevant roof area unless detailed calculations are made, in which case up to 15% may be allowed. The same approach should be considered when the diaphragm effect is applied to facades. Careful design, calculation, and detailing should be done for doors and windows.
Buildings designed on stressed skin principles should normally be umbrella type structures rather than structures which carry fixed loads. In order to ensure the safety of the building at all times, the following restrictions should be placed on design:
a. Most of the load on the building should be applied via the sheeting itself, e.g. self weight, snow load, wind load.
b. If the sheeting is removed, most of the load will also be removed.
c. Sheeting should not be used for helping to resist other fixed loads, e.g. mechanical plant.
d. Sheeting must be regarded as a structural member and so must not be removed without proper consideration.
e. The calculations and drawings should clearly draw attention to the fact that the building is designed by stressed skin methods.
f. It should be made clear to the building owner and final users that roofing and/or facade design, calculation, and erection have been based on stressed skin principles in case of future modification or renovation.
Paragraph 9.17 of EN 1090 - 4 states:
"It is necessary to mark the areas of the diaphragms (structural class I) in the envelope
- as 'diaphragm' on the layout drawing and
- in the operations and maintenance manual and
- with clearly visible, permanent warning signs on the finished construction (example image below).
The text on the sign shall indicate that the stability of the whole building will be at risk if alterations are subsequently undertaken to the diaphragms without static analysis. The information in the operations and maintenance manual shall indicate that the stability of the whole building will be at risk if alterations are subsequently undertaken to the diaphragms without a suitable analysis.
The owner of the building has to be informed about size, position, and significance of the diaphragm."
1.4 Types of diaphragm
Sheeting may span perpendicular to the length of the building (see Figure 3) or parallel to the length of the building (see Figure 4). Whenever possible, each panel of sheeting should be fastened on all four edge members since this gives the greatest diaphragm resistance and stiffness. If all members are not at the same level, 'shear connectors,' as shown in Figure 5, may be used to provide fastening on all four sides. If this is not possible, diaphragms may be fastened to purlins on two edges only provided that the end panels are fastened on their third side to the end gables. If sheeting is fastened only to the purlins, then the purlin/rafter connections at the intermediate rafters must be adequate to introduce the loads at these rafters into the diaphragm.
The typical diaphragm panel shown in Figure 5 is for sheeting spanning perpendicular to the length of the building. In calculating the shear resistance and flexibility of a panel, the design expressions refer to the direction parallel to the corrugations. For sheeting spanning parallel to the length of the building, a modification to the design expressions must be made. This modification is not considered in this lecture.