Built-up Members in Plastic Design

ULTIMATE STRENGTH DESIGN CURVES FOR

LONGITUDINALLY STIFFENED PLATE PANELS WITH LARGE bit

by

Joseph F. Vojta

and

Alexis Ostapenko

This work has been carried out as part of an investigationsponsored by the Department of the Navy with funds furnished by theNaval Ship Engineering Center Contract Nobs - 94092.

Reproduction of this report in whole or in part is permittedfor any purpose of the United States Government.

Qualified requesters may obtain copies of this report fromthe Defense Documentation Center.

Fritz Engineering Laboratory

Department of Civil Engineering

Lehigh University

Bethlehem, Pennsylvania

August, 1967

Fritz Engineering Laboratory Report No. 248.19

248.19

TAB LEO F CON TEN T S

i

Page

l. INTRODUCTION 1

2. PRELIMINARY CONCEPrS 2

3. METHOD OF USING THE ULTIMATE STRENGTH DESIGN CURVES 4

4. SYMBOLS 11

5. FIGURES 13

6. ACKNOWLEDGMENTS 19

-248.19 -1

1. I N T ROD U C T ION

The purpose of the ultimate strength design curves presented

here is to rapidly determine the dimensions of a longitudinally stiff-

ened plate panel that will just sustain a simultaneous axial and lateral

loading. Given a set of loads and overall dimensions and assuming some

relative proportions of the cross section, the dimensions of the cross

section can be found. A series of different sets of relative proportions

can be assumed and the most advantageous section selected from these.

The dimensions and range of loads for which these curveS apply

are those used in ship bottom plating.

The theory and the computer program used in obtaining the data

for these design curves are described in ULT:MATE STRENGTH DESIGN OF

*LONGITUDINALLY STIFFENED PLATE PANELS WITH LARGE bit .

* Vojta, J. F. and Ostapenko, A.ULTIMATE STRENGTH DESIGN OF LONGITUDINALLY STIFFENED PLATEPANELS WITH LARGE bit, Fritz Laboratory Report No. 248.18,Lehigh University, August, 1967.

248.19

2. PRE LIM I N A R Y CON C E P T S

-2

The type of cross section analyzed consists of a plate stiff-

ened by a series of tee-stiffeners, (Fig. 1). The loads considered are

a compressive axial load, pI, acting in the direction of the stiffeners

and a uniformly distributed lateral load, q, on the plate side of the

cross section causing compression in the plate at the. middle of the span

during bending (Fig. 2). The ends A and B can either be both fixed or

both simply-supported. There are two sets of curves, one for each end

condition; .however , their use follows identical procedures.

An idealized cross section shown in Fig. 3 is used in the

design curves and for the calculations of the required cross section.

In non-dimensional terms it can be described by the parameters A IA ,s p

The desig~ curves apply when bit is large enough (bit ~ 45)

for the plate to buckle before the ultimate load is reached i

The following ranges of values were used in the development of

the design curves:

A IA = 0.20 to 0.48s p

AflAs0.35 to 0.60

bit 60 to 110

248.19 -3

Q = q(~) 40 to 480t

o /0 = 0.00 to 0.15r yp

However, extrapolations outside these ranges can be used in most cases.

The following values are assumed as fixed in the development

of the curves:

Yield stress of plate and stiffener, 0 = 0 = 47.0 ksi.. ys yp

Modulus of elasticity, E = 29,600 ksi

Poisson's Ratio, ~ = 0.30.

248.19

3. MET HOD o F U SIN G THE ULTIMATE

-4

STRENGTH DESIGN CUR V E S

The use of the design curves will now be illustrated sche-

matically. This is followed by the procedure outlined in steps and by

a numerical example.

3.1 Schematic Example

Known from the loading, geometry and material conditions are

the parameters:

B = Total panel width (in. )

t Length of section (in.)

pI Total panel axial load (kips)

or = Plate compressive residual stress (ksi)

° Plate yield stress (ksi)yp

° Stiffener yield stress (ksi)ys

E = Modulus of elasticity (ksi)

The geometric parameters AsIA p ' AfiAs' bit and dlt are all assumed.

Dimensions of the cross section can be obtained through the use of the

design curves which find the plate width, b. This can be repeated many

times with different assumed parameters and the most advantageous section

can be selected depending upon the criteria required.

248.19 -5

Figure 4 shows a schematic sketch of the design curves. Begin-

ning in Box "A", compute 8 for the chosen values of bIt and d/t. For

bIt < 80 use 82 on the bottom scale as a starting point; for bIt > 80

use 81

on the top scale. Assuming d/t, compute Q

Qd

q(-)t

( 1)

Project a vertical line to the curve with the correct residual stress

*ratio 0 /0 and the correct Q. A horizontal line is then to be drawnr yp

to the right for bIt > 80, following dotted lines, (or to the left for

bIt ~ 80, solid lines).

The intercept on the N axis (N' value in Fig. 4) is a value

based on Af/As = 0.60. If the designer chooses these values for the

cross section, he can stop here and compute b as follows:

b (inches) 0.0003895 (pI (b/t)2) for s. s. endsB N

(2)

b (inches) 0.001287P' (bit) 1.65 .

( - - ) for fixed endsB N

If different values of As/A p and Af/As are chosen, the cross section must

be modified in Boxes "B" and "C".

For As/Ap 1 0.34 and Af/As 1 0.60, the designer continues the

horizontal line through the N axis to the curve corresponding to the cor-

rect Q and A /A in Box "B". A vertical line from here will·intercepts p

the R axis at a value pertaining to Af/A = 0.60, with A /A , bIt,ssp

* Interpolation between curves for Q varies approximately with thelogarithm of Q. All other interpolations are approximately linear.

248.19 -6

and d/t as previously chosen. However, since R is a complicated term,

not readily useful for computing b, one should continue on to Box "e" in

all cases.

After locating the correct curve in Box "e", the vertical line

through the R axis should be extended until it intersects this curve. A

horizontal line will now give a value on the N axis. The plate width b

can then be found from Eqs. 4 to 5:

b (inches) 0.000223 (pI (bit) \ for s. s. ends (4)B N

b (inches) 0.0017246fl (blt)1.65

for fixed ends (5)( B N )

Having obtained b from one of the equations of Eqs. 2 to 5, the

area values can now be computed for the idealized cross section as follows:

Plate area, Ap

(6)

Stiffener area, As

(7)

Stiffener flange area, Af = (-~f) As = (~f) (~s) r.(~~t)J (8)s . s p L

As [ Af )] [b2 JWeb area, A A - Af = ( A

p) 1 -(As (bit)w s

A

h~~t) ]Total area, A A +A [1 +( AS)]s p p

(9)

(10)

The dimensions of the idealized cross section are:

Plate width (center to center of stiffeners), b(in.), from

Eqs. 2 to 5.

248.19

Plate thickness (in.), t

Stiffener depth (in.), d

b(bit)

= (dlt) b(bit)

-7

(11)

(12)

Aw

Web plate thickness, (in.), w = d = (dlt)(13)

The stiffener flange can be proportioned as desired as long as its area

is as given by Eq. 8.

Figure 5 presents the design curves for panels with simp1y-

supported ends; Fig. 6 presents the design curves for fixed ends.

3.2 Detailed Outline of Steps to Follow

1.

0" 10r yp

Assume dlt,blt, A IA , and Af/A and compute S, Q,s p s

The formula for S is given on the design charts.

Q q (dlt) (q in psi) From Eq. (1)

47.0 is the yield stress for which

these curves are valid.

2. Pick the correct scale for the starting point S depend-

ing upon bit < 80 or bit ~ 80. Draw a vertical line from S to

the correct curve.

3. Draw a horizontal to the N axis; to the right for bit < 80

or to the left for bit> 80.

4. If As/Ap = 0.34 and Af/As

or 3 then go to Step 8.

0.60, compute b from Eq. 2

248.19

If either As/Ap I 0.34 or Af/As I 0.60 ~roject a hori­

zontal line to the curve corresponding to the chosen A /A .s p

5. Draw a ve~tical line to the curve corresponding to the

6. Draw a horizontal line to the N axis.

7 . Compute b from Eq. 4 to 5.

8~ Compute areas (Eq. 6-to 10) and cross-sectional dimen-

sions (Eqs. 11 to 13).

3.3 Numerical Example

Given: Panel with fixed ends Q 11.25 psi

P' 12,800 kips (J 0.000 psir

B = 41'-8" 500 in. a a 47.0yp ys

t 22'-8" 272 in.

Solution:

-8

Assume: b/t = 60, dlt A/A = 0.48s p

1.a

rCompute S, Q, , and use the design curves for fixedayp

ends, Fig. 6.

S 45.0 jp, B

(dlt)0.65

j 500 (272): 45.0 0 65

12800 (16)(60) .9.675

248.19

Qd

q (t)= 11.25 (16) 180.0

-9

Or 0.000= ~--=--a 47.0yp

0.000

2. Since bit < 80, the lower scale is used. A line is drawn

upward to the curve for Q =180, a 10 = 0.000 (solid line).r yp

3. Draw a horizontal line to the right (bit < 80) which gives

N 0.676.

4. Both As/Ap and Af/As were chosen not to be the standard

values, thus a horizontal line is drawn to the right to the curve

for A IA = 0:48, Q = 180.s p

5. A vertical line is drawn down to' the curve for Af/As

0.35. (This intercepts the R axis at R = 32.05).

6. Draw a horizontal line to the left giving N = 0.653.

7. From Eq. 5

b ~ 0.0017246 [P'(~) 1. 6:0 ]=BN~ + (AS)]

P

(12800) (60)1.650 _0.0017246 [500 (0.653) (1.48)]- 39.0 in.

8. Compute the values of the areas of the cross section

Ab2 (39.0 in)2

25.35 in2 from Eq. 6p =(bit) 60.

A= 0.48 (25.35 in

2)

2A = (AS) A 12.17 in from Eq. 7s pp

248.19

0.35 (12.17 in2

) = 4.26 in2

-10

from Eq. 8

A = A - Aw s f 12.17 in

2- 4.26 in

2= 7.91 in2

from Eq. 9

Total area = A + A = 12.17 in2 + 25.35 in

2s p

37.52 in2

from Eq. 10

Note: These values are for the idealized cross section. For the total

500panel the values are multiplied by Bib = 39.0 = 12.82 ~ 13.

Computation of the idealized cross section:

b 39.0 in. as computed in Step 7.

t = b(bit) =

39.0 in60

0.65 in from Eq. 11

d = t(d/t) = 0.65 in (16.) = 10.4 in from Eq. 12

0.48 (1-0.35)16.0 39.0

0.761 in from :Eq. 13

Arbitrarily let the stiffener flange be 3/4 in. thick (that

4.62 in20.75 in = 5.68 in.

The idealized cross section for this example is shown in Fig. 7. The

total panel will then consist of a plate 500 inches wide with stiffeners

spaced 39 in. center to center.

248.19 -11

4. S Y M B 0 L S

A Total area of idealized cross section.

Af

Area of flange, idealized cross section

A Area of plate, idealized cross sectionp

A Area of stiffener, idealized cross sections

A Area of web, idealized cross sectionw

B Total panel width

b Width of idealized cross section, i.e. center to center of stiff-

eners

E

N,R,S,

m

P'

Q

q

t

w

Width of stiffener flange

Depth of cross section

Modulus of elasticity

Length of panel

Values from design charts

Bending moment acting on total panel cross section

Axial load (kips) on total panel cross section

q (d/t)

Uniformly distributed lateral load (psi)

Thickness of plate

Thickness of stiffener flange

Thickness of stiffener web

Poisson's Ratio

Compressive residual stress in plate (ksi)

248.19 -12

4. S Y MBa L S (continued)

cr Yield stress of plateyp

cr Yield stress of stiffenerys

248.19

5. FIG U RES

-13

248.19

Fig. 1 General Cross Section

-14

p,~ml

,q

ml

j..

Fig. 2 Loading Condition

..I ~ Symm.

d

Ap= bt

Af =bf tf

Aw=dw

As =bf tf+ dw

A =bt + bf tf + dw

I.. b~I

Fig. 3 Idealized Cross Section

I'-J

bIt ~ 80 S. bIt ~ 80 .po00.t-'\0

Box ItB" Box "BIIModification ModificationFor As/Ap Box "AIt

N~'For As/Ap

N·(Sta r t)

• I II It tI I

R. I I R2

bIt < 80 S2 bIt < 80 II

Box lie II I Box He"Modification • ModificationFor AtlAs I For Af/A s

N.IIN2

Fig. 4 Schematic Plot of Design Curves It-'VI

248.19/ -16

9;2" 8a /6'L., $.:8/.8 V pyo/J'.J!'4;.../

6' /0 /4 /8 .e.e

0.://0

/.0

a6'

O"'R = 0.000O"'yp

___ _ _ O"'R =0.075. O"'yp .

___ O"'R =0.150O"'yp

0=40=110=180'=320

1.0

0.8

N

0.6

0.4

0.2

bit < 80.AA~ =0.20

As---- A=0.34

p

As--- -,;:-=0.48

p

0=40

0=110

:: =0.35

:: =0.60

0=40

Q=IIO

bit < 80.

0=180

0=320

~~~==--AS/Ap =.48

~~~~~ AS/Ap =.20

ol...-_L-_..L-_..L..-_..L..-_..L..-_-'--_-'--_-'--_-'--_~

1.0

1.2

0.4

0.2

0.8

N

0.6

q = La teral load (psi)

L =Panel length (in.)

b = 0.000223 BN{I+ As lAp)

pi = Axial force on panel (kips)

B = Total panel width (in·.)

o = q (d/t) , psi

26 22 18

bit < 80. 5 = 81.8 JI(d~)~b/t) bit < 80.

DESIGN CURVES FOR SIMPLY - SUPPORTED ENDSI. Assume bit, d/t, AsIAp , AflAs2. Compute 5,0, O"'R/O"'yp

3. Start in plot above:Use lower scale for bit < 80.Use upper scale for bit ~ 80.

4. Use curves on right for bit < 80.Use curves on left for bit ~ 80.

5. Find final N· value

6. Compute b: .P'{b/t)

/.0

a6'

As/Z~-/~----+-'7"""I-""7""I'+=7t---:.~/f7-~~p':.4'8

"."../ A~.:•.eO

/00

Fig. 5 Design Curves for Simply-Supported Ends

-17

Q =40

:: = 0.35

AfI-A =0.60, s

__ :s =0.20p

As---- Ap =0.34

As,--- -A- =0.48

p

R

bit < 80.

\\\\\\\

\

N

0.6

0.2

0.4

0.8bit < 80.

ENDS

q =Lateral load (psi)

L = Panel length (in.)

~Q=40=110

.=180=320

--- O""R. = 0.000O""yp

_____ O""R .. =0.075O""yp

O""R~-- ~ =0.150

yp

I. Assume bit, dlt, AsIAp , AflAs

2. Compute 5, Q, O""R/O""yp

3. Start in plot above:Use lower scale for bit < 80.Use uppel! scale for bit ~ 80.

4. Use curves 01':1 right for bit < 80.Use curvesoli'l left for bit ~ 80.

5. Find final N value

6. Compute b:_ f l (b/t)I.650

b- 0.001724 aN(I + As/Ap)

L BL 4/ 2' 80S.: 45:0 ¥ ;14j/~b4/0.65

/4 /8 22 26

26 22 18

A' BL5::: 45.0 pi(~)(b/t)0.65

DESIGN CURVES FOR FIXE 0

pi = Axial force on panel (kips)

B = Total panel width (in.)

Q =q (d/t) , psi

bit < 80.

IV

06

0.:/80 C/.4

0.:320

0.:40

0.://0

0.:40

248.19

Fig. 6 De~ign Curves for Fixed Ends

248.19

5.68"

H0.75"+

0.761" 10.4"

-18

0.65" =}= C:=:======~====-============::::::J

L_~39.:.=--.01l~JFig. 7 Cross Section - Numerical Example

248.19 -19

6. A C K NOW LED G MEN T S

This report is part of a research project on Built-Up Members

in Plastic Design carried out at Fritz Engineering Laboratory, Lehigh

University, Bethlehem, Pennsylvania. Dr. A. Ostapenko is Director of the

Project. Dr. L. S. Beedle is Director of the Laboratory and Acting Head

of the Department of Civil Engineering. The project sponsor is the Naval

Ship Engineering Center, Department of the Navy. The authors are thank­

ful for their support, and in particular to Mr. John Vasta who initiated

this project.

The authors gratefully acknowledge the advice and able assistance

of Dr. Leonard A. Lopez. For their assistance in the development of the

data for this report many thanks are extended to Messrs. R. A. Strawbridge

and D. Fahringer and to Mrs. Chenchang Ho Ko.

The authors are also indebted to Mr. John M. Gera, JF. and Miss

Sharon D. Gubich for preparing the drawings and to Miss Linda E. Nuss for

typing the manuscript.

UNCLASSIFIEDSecurltv Clossificat on

DOCUMENT CONTROL DATA· R&D(Seeurlry cI....lfle..llon 01 It"e, body 01 ..b.tr..cl and Inded"l/ ..nn""""dn mu!'t be entewd wl.en tI,e overall report Is clossllled)

I. ORIGINATING ACTIVITY (Corpora,e ..uthor) '. Za. REPORT SECURITY CLASSIFICATION

Fritz Engineering Laboratory UNCLASSIFIEDDepartment of Civil Engineering t-:Z7b-.":'G":'R":'O-U':-P----------------1

Lehigh University .Bethlehem Pennsv1vania

3. REPORT TITLE

ULTIMATE STRENGTH DESIGN CURVES FOR LONGITUDINALLY STIFFENED PLATE PANELS WITHLARGE bit

•• QESCRIPTIVE NqT.EII (7'yPf. 01 )~oft ..nrl'nc'u't've dale.h. A presenta~~on OL u ~~ma~e s~rengt design curves for longitudinally stiffened plate

Dane1s with large b tII. AUTHORtSI (Fir.' n ..me, middle Inlll.. I, I... , n ..me)

Joseph F. VojtaAlexis Ostapenko

0. REPORT DATE 7... TOTAl. NO. OF PAGES 17b. NO. OF REFS

August, 1967 19 NoneII... CONTRACT OR GRANT NO. II... ORIGINATOR'S REPORT NUMBERIIII

Nobs-94092 .b. PRO.lECT NO. 248.19

S.F. 103-03-01, Task 1974c. lib. OTHER REPORT NOISI (Any other number. th.. t m..y be ....IQned'hi. report)

d.

10. DIIITRIBUTION STATEMENT

Qualified requesters may obtain copies of this report from the DefenseDocumentation Center

11. SUPPLEMENTARY NOTEII

13. A BSTRAC T

12. SPONSORING MILITARY ACTIVITY

Department of the NavyNaval Ship Engineering CenterWashington, D. C.

This report presents ultimate strength design curves for longitudinallystiffened plate panels as used in ship bottom plating. The curves determinethe dimensions of a plate panel that will just sustain a given simultaneousaxial and lateral loading condition. Repeated use of the curves will give ·theoptimum cross section.

The theory and computer program used for gathering data for these curvesare described in Fritz Laboratory Report 248.18, ULTIMATE STRENGTH DESIGN OFLONGITUDINALLY STIFFENED PLATE PANELS WITH LARGE bit, by J. F. Vojta andA. Ostapenko, Lehigh University, August, 1967.

UNCLASSIFIEDSecurity ClassiCication

Security Classification

,.. LINK" LINK B LINK CKEY WORDS

I . ROLE WT ROLE WT ROLE WT

"

combined loads, design curves, longitudinalstiffeners, ship plates, ultimate strength

)

,

.

-

:

Security Classification

Voj ta, Joseph F. andOstapenko, Alexis

VOjta, Joseph F. andOs-tapenko, Alexis

I.

II. S.F. 103-03-01Task 1974

KEY WORDScombined loads, designcurves, longitUdinalstiffeners, ship plates,ultimate strength

KEY WORDScombined loads, designcurves, longitudinalstiffeners, ship plates,ultimate strength

II. S.F. 103-03-01Taak 1974

1.

-----[-----l

Fritz Engineering Laboratory Report No. 248.19ULTIMATE STRENGTH DESIGN CURVES FOR LONGITUDINALLY STIFFENED PLATEPANELS WITH LARGE b It byJoseph F. Vojta and Alexis Ostapenko. Aug. 1967, v, 19p. J illus.,design curves.

This report presents ultimate strength design curves forlongitudinally stiffened plate panels as used in ship bottexn plating.The curves determine the dimensions of a plate panel that will justsustain a given simultaneous axial and lateral loading condi tion ..Repeated use of the curves will give the optimwn cross section.

The theory and computer program used ·for gathering data forthese curves are described in Fritz Laboratory Report 248 .. 18,ULTIMATE STRENGTH DESIGN OF LONGITUDINALLY STIFFENED PLATE PANELS,WITH LARGE bIt, by J. F .. Vojta and A. Ostapenko, Lehigh University,August, 1967.

Fritz Engineering Laboratory Report No. 248.19ULTIMATE STRENGTH DESIGN CURVES FOR LONGITUDINALLY STIFFENED PLATEPANELS WITH LARGE bit byJoseph F. Vojta and Alexis Ostapenko. Aug. 1967, v, 19p., illus.,design curves ..

This report presents ultili:tate strength design curves forlongitudinally stiffened plate panels as used in ship bottexn plating.The curves determine the dimensions of a plate panel that will justsustain a given simultaneous axial and lateral loading condition.Repeated use of the curves will give the optimum. cross section.

The theory and computer program used ·for gathering data forthese curves are described in Fritz Laboratory Report 248.18,ULTIMATE STRENGTH DESIGN OF LONGITUDINALLY STIFFENED PLATE PAIlELS,WITH LARGE bIt, by J. F. Vojta and A. Ostapenko, Lehigh University,August, 1967 •.

.,.-----------IIIIIIIIIIII1- 1-----1

IIIIIIIIII_L ~

Vojta, Joseph F. andOstapenko, Alexis

Vojta, Joseph F. andOstapenko, Alexis

KEY WORDScombined loads, designcurves, longitudinalstiffeners, ship plates,ultimate strength

II. S.F. 103-03-01Task 1974

II. S.F. 103-03-01Task 1974

KEY WORDScombined loads, designcurves, longitudinalstiffeners, ship plates,ultimate strength

1.

1.

STIFFENED PLATE

Ostapenko .. Aug .. 1967, v, 19p., illus .. ,

Fritz Engineering Laboratory Report No. 248.19ULTDIATE STRENGTH DESIGN CURVES FOR LONGITUDINALLY STIFFENED PLATEPANELS WITH LARGE bIt byJoseph F. Vojta and Alexis Ostapenko. Aug. 1967 ~ v. 19p., l11us.,design curves.

This report presents ultimate strength design curves forlongitudinally stiffened plate panels as used in ship bottan plating.The curves determine the dimensions of a plate panel that will justsustain a given simultaneous axial and lateral loading condition.Repeated use of the curves will give the optimum. cross section.

Fritz Engineering Laboratory Report No. 248.19ULTIMATE STRENGTH DESIGN CURVES FOR LONGITUDINALLYPANELS WITH LARGE b It byJoseph F. Vojta and Alexisdesign curves.

The theory and computer program used ·for gathering data forthese curves are described in Fritz Laboratory Report 248.18,ULTIMATE STRENGTH DESIGN OF LONGITUDINALLY STIFFENED PLATE PAIlELS,WITH LARGE bIt, by J. F. Vojta and A. Ostapenko, Lehigh University,August, 1967.

This report presents ultimate strength design curves forlongitudinally stiffened plate panels as used in ship bottexn plating.The curves determine the dimensions of a plate panel that will justsustain c: given simultaneous axial and lateral loading condition..Repeated use of the curves will give the optimum. cross section.

The theory and computer program used ·for gathering data forthese curves are described in Fritz Laboratory Report 248.18,ULTIMATE STRENGTH DESIGN OF LONGITUDINALLY STIFFENED PLATE PAIlELS,WITH LARGE bIt, by J .. F. Vojta and A. Ostapenko, Lehigh UniverSity,August, 1967.

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