corrugated sheet

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10Corrugated Sheets

10.1 GENERAL REMARKS

Corrugated sheets (Fig. 10.1) have been used in building construction sinceabout 1784. This is one of the oldest types of cold-formed steel products. At

present, numerous types of corrugated sheets with different coatings are beingproduced by many manufacturers. Several standard corrugated steel sheets aregenerally available for building construction and other usage.

In general, the design methods described in previous chapters are alsoapplicable to the design and use of corrugated steel sheets. However, certainsimplified formulas for computing the sectional properties of standard cor-rugated steel sheets can be used in design. Following an investigation con-ducted by the AISI during 19551957, a publication entitled Sectional

Properties of Corrugated Steel Sheets was issued by the Institute in 1964 toprovide the necessary design information for corrugated sheets.1.87

This chapter is intended to discuss the application of arc-and-tangent-typecorrugated steel sheets and trapezoidal-type corrugated sheets (Fig. 10.2) andthe design of such cold-formed steel products. The information includedherein is based on AISI publications1.871.89 and other references used in thischapter.

10.2 APPLICATIONS

Corrugated steel sheets are frequently used for roofing and siding in buildingsbecause the sheets are strong, lightweight, and easy to erect. In many casesthey are used as shear diaphragms to replace conventional bracing and tostabilize entire structures or individual members such as columns and beams.The shear diaphragms and diaphragm-braced beams and columns were dis-

cussed in Chap. 9.Figure 1.18a shows the use of standard corrugated sheets for exterior cur-

tain wall panels. The application of unusually large corrugated sections inframeless stressed-skin construction is shown in Fig. 1.18b. In addition, cor-rugated steel pipe of galvanized sheets has long been used in drainage struc-tures for railways, highways, and airports.1.18,1.88,1.89 Figure 10.3 shows typicalcorrugated metal pipe culvert used for highway systems. Other corrugatedsteel products have been used for retaining walls, guardrails, conveyer covers,

aerial conduits, and other purposes.1.18,1.88


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10.3 SECTIONAL PROPERTIES AND DESIGN 589

Figure 10.1 Cross section of typical arc-and-tangent-type corrugated sheets.

Figure 10.2 Cross section of typical trapezoidal-type corrugated sheets.

During recent years, corrugated sheets have been used in flooring systemsfor buildings and bridge construction.1.88,10.1 These products have also beenused as web elements for built-up girders in order to increase web stiffnessinstead of using a relatively thicker plate or a thin web with stiffeners. The

Macomber Panlweb girder shown in Fig. 10.4 consists of 0.075- to 0.15-in.(1.9- to 3.8-mm) corrugated web for depths of 20 to 40 in. (0.51 to 1.02m).10.2 Reference 10.3 discusses the required connections for beams with cor-rugated webs. The fatigue strength of girders with corrugated webs was re-ported in Ref. 10.4.

10.3 SECTIONAL PROPERTIES AND DESIGN OF ARC-AND-

TANGENT-TYPE CORRUGATED SHEETS

In 1934 Blodgett developed a method to compute the sectional properties ofarc-and-tangent-type corrugated sheets.10.5 The computation of the moment ofinertia and the section modulus for standard corrugated sheets has been sim-plified by Wolford.10.6 In the computation, design curves and tables can beused to determine factors C5 and C6 in Eqs. (10.1) and (10.2):

1.87

3 2

I

C bt

C bd t (10.1)5 6

2IS (10.2)

d t

where I moment of inertia, in.4

S section modulus, in.3

b width of sheet, in.

d depth of corrugation, in.t thickness of sheet, in.


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590 CORRUGATED SHEETS

Figure 10.3 Typical corrugated metal pipe culvert installation on interstate highway

system.1.87

Figure 10.4 Macomber Panlweb girder.10.2


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Figure 10.5 Radius-to-depth ratio versus pitch-to-depth ratio at various web an-gles.10.6

C5, C6 factors depending on shape of arc-and-tangent-type corrugation.

Using Wolfords charts, as shown in Figs. 10.5 to 10.9, the values of themoment of inertia, section modulus, area, radius of gyration, and length of

tangent can be computed by the following procedure:

1. Compute the midthickness radius R,

tR R

2

2. Compute values of q and K,

R pq and Kd d

where p is the pitch.

3. From Fig. 10.5, determine the angle for the computed values of qand K.

4. From Figs. 10.6 and 10.7, determine C5 and C6 by using K and angle.

5. From Figs. 10.8 and 10.9, determine and the m /d ratio.6. Compute I and S by using Eqs. (10.1) and (10.2).

7. Compute

A bt

8. The radius of gyration is

Ir

A9. The length of the tangent is d

m

d


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Figure 10.6 Factor C5 versus pitch-to-depth ratio at various web angles.10.6

Figure 10.7 Factor C6

versus pitch-to-depth ratio at various web angles.10.6

Based on the method outlined above, the sectional properties of severaltypes of corrugated sheets have been developed and published in Refs. 1.87and 1.88. The accuracy of Eqs. (10.1) and (10.2) has been verified by beamtests conducted under the sponsorship of the AISI. Some of the sectionalproperties for galvanized and uncoated corrugated sheets are reproduced in

Tables 10.1 to 10.4. In these tables, the pitch of corrugation ranges from 114to 6 in. (32 to 152 mm), and the depth varies from to 2 in. (6.4 to 51 mm).14The thickness of steel sheets varies from 0.0135 to 0.276 in. (0.3 to 7 mm).The inelastic flexural stability of corrugations was studied by Cary in Ref.10.11.

In determining the load-carrying capacity of corrugated sheets, the nominalflexural strength can be computed in a conventional manner as follows:


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Figure 10.8 Factor versus pitch-to-depth ratio at various web angles.10.6

Figure 10.9 Tangent-to-depth ratio versus pitch-to-depth ratio at various web an-gles.10.6

M SFn y

where S

section modulus obtained from Tables 10.1 to 10.4Fy yield point of steel

The design flexural strength can be computed by using b 1.67 for ASDand b 0.95 for LRFD.

With regard to the deflection requirements, more deflection may be per-mitted for corrugated sheets than for other types of members. However, itshould not exceed 1/90 of the span length due to the possible leakage at end

laps or loss of end connections.


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TABLE 10.1 Sectional Properties, per Foot of Corrugated Width, of Several Types of Corr

Galvanized

Sheet

Thickness,

(in.)

p 1 in., d in.1 1 4 4

A (in.2) I (in.4) S (in.3)

p 2 in., d in.2 1 3 2

A (in.2) I (in.4) S (in.3)

p 2 in.,2 3

A (in.2) I (in

0.1084

0.0785

0.0635

0.05160.0396

1.396

1.004

0.807

0.6510.493

0.0120

0.00811

0.00636

0.005040.00377

0.0675

0.0497

0.0408

0.03370.0262

1.379

0.991

0.797

0.6430.487

0.0417

0.0295

0.0236

0.01890.0143

0.138

0.102

0.0839

0.06880.0532

1.439

1.035

0.832

0.6710.508

0.068

0.048

0.038

0.0310.023

0.0336

0.0276

0.0217

0.0187

0.0172

0.415

0.336

0.259

0.219

0.199

0.00315

0.00254

0.00195

0.00165

0.00150

0.0224

0.0185

0.0145

0.0124

0.0113

0.410

0.332

0.225

0.216

0.197

0.0120

0.00971

0.00746

0.00632

0.00575

0.0451

0.0369

0.0287

0.0245

0.0223

0.427

0.346

0.266

0.226

0.206

0.019

0.016

0.012

0.010

0.009


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TABLE 10.1 (Continued)

Galvanized

SheetThickness,

(in.)

p 2 in., d in.2 7 3 8

A (in.2) I (in.4) S (in.3)

p 3 in., d in.58

A (in.2) I (in.4) S (in

0.1084

0.0785

0.0635

0.0516

0.0396

1.583

1.138

0.915

0.738

0.560

0.1471

0.1050

0.0843

0.0679

0.0514

0.300

0.221

0.180

0.147

0.113

1.411

1.014

0.816

0.658

0.499

0.0706

0.0502

0.0402

0.0323

0.0244

0.193

0.143

0.117

0.095

0.073

0.0336

0.0276

0.0217

0.0187

0.0172

0.470

0.381

0.293

0.249

0.226

0.0432

0.0350

0.0269

0.0228

0.0207

0.0952

0.0776

0.0601

0.0511

0.0466

0.419

0.339

0.261

0.221

0.202

0.0205

0.0166

0.0128

0.0108

0.00986

0.062

0.051

0.039

0.033

0.030

Notes:

1. p corrugation pitch; d corrugation depth.

2. Steel thicknesses upon which sectional properties were based were obtained by subtracting 0.0020 in. fro

allowance applies particularly to the 1.25-oz coating class (commercial).

3. Blodgetts formula was used to compute I (see Ref. 10.6).4. 1 in 25.4 mm.


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TABLE 10.2 Sectional Properties, per Foot of Corrugated Width, of Several Types of Corr

Uncoated

Sheet

Thickness,

(in.)

p 1 in., d in.1 1 4 4

A (in.2) I (in.4) S (in.3)

p 2 in., d in.2 1 3 2

A (in.2) I (in.4) S (in.3)

p 2 in.,2 3

A (in.2) I (in

0.1046

0.0747

0.0598

0.04780.0359

1.372

0.980

0.784

0.6270.471

0.0118

0.00789

0.00616

0.004850.00360

0.0665

0.0486

0.0398

0.03260.0252

1.356

0.968

0.775

0.6200.465

0.0410

0.0288

0.0229

0.01820.0136

0.136

0.100

0.0818

0.06650.0509

1.412

1.008

0.807

0.6450.485

0.067

0.047

0.037

0.0300.022

0.0299

0.0239

0.0179

0.0149

0.0135

0.392

0.312

0.235

0.195

0.177

0.00298

0.00236

0.00177

0.00147

0.00133

0.0213

0.0172

0.0132

0.0111

0.0101

0.388

0.310

0.232

0.193

0.175

0.0113

0.00906

0.00678

0.00564

0.00511

0.0428

0.0346

0.0262

0.0219

0.0199

0.404

0.323

0.242

0.201

0.182

0.018

0.015

0.011

0.009

0.008


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TABLE 10.2 (Continued)

Uncoated

SheetThickness,

(in.)

p 2 in., d in.2 7 3 8

A (in.2) I (in.4) S (in.3)

p 3 in., d in.58

A (in.2) I (in.4) S (in

0.1046

0.0747

0.0598

0.0478

0.0359

1.556

1.112

0.890

0.711

0.534

0.145

0.103

0.0819

0.0654

0.0490

0.295

0.216

0.175

0.142

0.108

1.387

0.990

0.793

0.634

0.476

0.0694

0.0490

0.0391

0.0312

0.0234

0.190

0.140

0.114

0.092

0.070

0.0299

0.0239

0.0179

0.0149

0.0135

0.445

0.356

0.266

0.222

0.201

0.0408

0.0326

0.0244

0.0203

0.0184

0.0902

0.0726

0.0547

0.0457

0.0415

0.396

0.317

0.237

0.198

0.179

0.0194

0.0155

0.0116

0.00967

0.00876

0.059

0.047

0.036

0.030

0.027

Notes:


2. Blodgetts formula was used to compute I (see Ref. 10.6).

3. 1 in. 25.4 mm.


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TABLE 10.3 Sectional Properties, per Foot of Corrugated Width, of Several

Types of Corrugated Steel Sheets for Culverts1.87

Sheet Thickness,

(in.)

Galvanized Uncoated

p 2 in., d in.2 1 3 2

A (in.2) I (in.4) S (in.3)

p 3 in., d 1 in.

A (in.2) I (in.2) S (in.3)

0.1681 0.1644 2.133 0.0687 0.207 2.458 0.301 0.517

0.1382 0.1345 1.744 0.0544 0.171 2.008 0.242 0.427

0.1084 0.1046 1.356 0.0411 0.136 1.560 0.186 0.336

0.0785 0.0747 0.968 0.0287 0.0998 1.113 0.131 0.243

0.0635 0.0598 0.775 0.0227 0.0812 0.890 0.104 0.196

0.0516 0.0478 0.619 0.0180 0.0659 0.711 0.0827 0.158

0.0396 0.0359 0.465 0.0135 0.0503 0.534 0.0618 0.119

Notes:


2. Steel thickness upon which sectional properties were based are from manufacturers standard

guage for carbon steel and are close to those obtained by subtracting 0.0037 in. from galvanized

sheet gauge thickness for galvanized coating of 2.00 oz/ft2 of double-exposed surfaces by

triple-spot test.

3. Blodgetts formula was used to compute I (see Ref. 10.6). Inside radii of corrugations were

taken as 11/16 and 9/16 in. for 2 and 3 1 in. corrugations, respectively.3 1 4 24. 1 in. 25.4 mm.

TABLE 10.4 Sectional Properties, per Foot of Corrugated Width, of SeveralTypes of Corrugated Steel Plates for Culverts1.88

Uncoated

Sheet

Thickness,

(in.)

p 5 in., d 1 in.

A (in.2) I (in.4) S (in.3)

Uncoated

Sheet

Thickness,

(in.)

p 6 in., d 2 in.

A (in.2) I (in.4) S (in.3)

0.1644 2.186 0.3011 0.5069 0.2758 4.119 1.990 1.749

0.1345 1.788 0.2438 0.4210 0.2451 3.658 1.754 1.562

0.1046 1.390 0.1878 0.3330 0.2145 3.199 1.523 1.376

0.0747 0.992 0.1331 0.2423 0.1838 2.739 1.296 1.187

0.0598 0.794 0.1062 0.1960 0.1644 2.449 1.154 1.066

0.1345 2.003 0.938 0.879

0.1046 1.556 0.725 0.689

Notes:


2. 1 in. 25.4 mm.


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10.4 SECTIONAL PROPERTIES AND DESIGN OF CORRUGATED SHEETS 599

The design of corrugated steel conduits is well discussed in Chap. 3 ofRef. 1.88.

10.4 SECTIONAL PROPERTIES AND DESIGN OFTRAPEZOIDAL-TYPE CORRUGATED SHEETS

Trapezoidal corrugated sheets (or ribbed panels) have often been used asroofing, floor deck, wall panels, bridge flooring, and permanent steel bridgedeck forms.

In the design of roofing, floor deck, and wall panels, the discussion onbeam strength and deflection presented in Chap. 4 can be used.

Steel bridge flooring has been used to carry live loads plus 30% for impactas well as the dead load of the surfacing material and the weight of the bridgeflooring. Permanent steel forms are designed for placement over or betweenstringers to carry the dead load of freshly poured concrete plus a 50-psfconstruction load. The AISI Specification1.314 can also be used for the designof steel bridge flooring and permanent steel forms. Additional information onthe design and installation of these products can be found in Refs. 1.88 and10.710.10.

The most favorable cross section of steel roof panels on the basis of min-imum-weight design is discussed in Ref. 1.247. During the past decade, ad-ditional studies have been made on the use of corrugated elements asstructural components. See Refs. 10.1210.18.

corrugated sheet

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