Local Buckling of Pultruded Beam(Bank LC)

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Construction and Budding Materials, Vol. 9, NO. 6, pp. 325-331, 1995

Copyright 0 1996 Elsevier Science Ltd

Printed in Great Britain. All rights reserved

095&0618/95/$10.00+0.00

0 9 5 0 - 0 6 1 8 ( 9 5 ) 0 0 0 5 1 - 8

Local buckling of pultruded beams -

nonlinearity, anisotropy and inhomogeneity

Lawrence C. Bank, Jiansheng Yin and Murali Nadipelli

Department of Civil Engineering, The Catholic University of America, Washington, DC

20064, USA

Received 21 October 1994; accepted 13 February 1995

Local buckling of pultruded fibre-reinforced plastic beams is discussed. The paper focuses on three

issues related to the prediction of buckling loads both from experimental data and from analytical

and numerical approaches, viz. nonlinearity, anisotropy and inhomogeneity. Experimental data

obtained from full-scale buckling tests are reviewed and a method proposed for estimating the

buckling stress in pultruded beams. Analytical studies based on classical orthotropic plate bucklingtheory are used to determine the edge restraint coefficient for pultruded beams and also to show

the influence of the in-plane material properties on the buckling loads. Numerical studies using the

finite element method in which inhomogeneous material properties in the beam cross-section are

considered are used to give predictions of buckling loads of the beams. Although the paper focuses

on local buckling of pultruded beams, it raises issues which are relevant to the analysis of pultruded

material structures of all types.

Keywords: pultruded beams; fibre-reinforced plastics; finite element analysis

Pultruded fibre-reinforced plastic (FRP) profile sections

have been produced for over 20 years in the United

States and in Europe. In recent years there has been

increased interest in the use of pultruded profiles in theconstruction industry for load-bearing structural appli-

cations in both building systems and bridges’. Primarily

motivated by their resistance to corrosion, engineers are

now discovering additional benefits of pultruded com-

posites which may include light weight, electromagnetic

transparency, damage tolerance, formability and

installed cost. Recent improvements in manufacturing

technology, particularly in the pultrusion method

(although also in the various resin transfer moulding

methods), have enabled the production of large cross-

sections (in the range of 1 m by 1 m) with relatively thick

walls (in the range of 25 mm) at relatively low cost ($4

to $6 per kg). Such large sized members are needed for

full-scale load-bearing civil engineering applications. The

low cost coupled with potentially low installation costs

due to light weight and customized profile shapes can

make pultruded composites viable structural materials.

Regardless of the form of the eventual profile, prior

to use as a structural component, a pultruded profile

currently needs to be tested at full-scale to validate its

structural performance. This is because at the present

time ‘reasonable doubt’ exists as to whether or not

structural behaviour can be predicted from knowledge

of the profile geometry and coupon test data. The pur-

pose of the current paper is to attempt to shed somelight on why such ‘doubts’ exist. Recently, a series of

controlled and extensively instrumented full-scale flex-

ural tests on a variety of pultruded beams was con-

ducted at the Catholic University of AmericazA. The

tests were conducted to investigate local buckling andultimate failure of the compression flange of commer-

cially produced wide flange I-shaped beam sections

when loaded in flexure. The purpose of the testing was

to develop a robust test methodology, to obtain test

data on local buckling and failure behaviour, and to

determine whether analytical and numerical methods

could be used to predict buckling loads based on

‘knowledge of the profile geometry and coupon test

data’. Although prior flexural testing of pultruded

beams has been conducted’ this work does not contain

the experimental detail needed in order to gain an in-

depth understanding of the phenomena discussed in this

paper. Since local buckling is one of the governing

design criteria for pultruded beams it was chosen for

this in-depth study. Other design criteria of importance

are lateral-torsional buckling6, ultimate failure, deflec-

tion, vibration, connection capacity and local bearing

capacity.

To meet these objectives a set of studies was con-

ducted to assess the significance of a number of factors

related to the local buckling characteristics of the pul-

truded beams tested. These were (i) the determination of

buckling load and buckling stress from experimental

nonlinear flange strain data, (ii) the effect of anisotropy

of the pultruded material and the edge restraint pro-vided by the web/flange junction, and (iii) the effect of

Construction and Building Materials 1995 Volume 9 Number 6 325



Local buckling of pultruded beams: L.C. Bank et al.

in-plane material inhomogeneity in the flanges and the

webs of the pultruded profile.

Nonlinearity

Tests were conducted on three types of standard pul-

truded FRP wide flange I-beams: (i) vinylester beams of

the 203 mm (8”) high and wide by 9.5 mm (3/8”) thick

series, (ii) polyester beams of the 203 mm (8”) high and

wide by 9.5 mm (3/8”) thick series, and (iii) vinylester

beams of the 203 mm (8”) high and wide by 12.7 mm

(112”) thick series. For identification purposes these will

be referred to as V 318, P 3/8, and V l/2, respectively.

Tests were conducted in a fixture especially designed to

produce local buckling in the beams in a controlled

fashion and to prevent ‘undesirable’ local instability

and failure modes from occurring. The beams were

simply supported and tested in four-point bending at a

span of 2743 mm (9 ft) with an interior constantmoment span of 1219 mm (4 ft). The beams were

monitored with strain and displacement indicators.

Full details of the testing methodology and descriptions

of the buckling and failure behaviour of the beams are

described in References 2-4. The load at which local

buckling occurred in the experiments was determined

from strain data obtained from back-to-back strain

gauges bonded on the top and bottom surfaces of the

compression flanges. The difference between the top

and bottom surface strain gauge data provides a conve-

nient way of detecting the instability in the compression

flange. A typical plot of the difference in strain data (S-

2-S-3) from ‘back-to-back’ strain gauges, one upper-

side (S-2) and one on the under-side (S-3) of the

compression flange, is shown in Figure 1 for one of the

P 318 beams (identified as P8-1 in Figure I). As can be

seen from Figure 1 the bifurcation in the strain data

occurs gradually over a range of load values and a

method is needed to precisely determine the buckling

load from plots of this type. Two methods were con-

sidered: an ‘estimation’ method and an ‘analytical’

method.

portion of the load-strain curve until it intersects the

straight line extending from the final post-buckled

(large deformation) linear portion of the curve. The

load thus obtained is referred to as the ‘estimated’ buck-

ling load. It is this load that has been previously

reported as the buckling load’s3 for the beams tested.

Buckling data for pultruded column tests have also

been obtained using this method7. Previously reported

local buckling data for beams’ was obtained by visual

observation of large post-buckled deformation and

therefore also represents this ‘estimated’ value.

Following careful examination of photographic data

of the buckled beams, such as that shown in Figure 2,

and considering the fact that the load versus strain

difference has a gradual slope change as the buckling

phenomenon initiates and then progresses into the post-

bucked regime, it was felt that a procedure was needed

to determine the ‘initial’ buckling load. This initial

buckling load was, therefore, determined analyticallyfrom the point at which the change in the initial linear

slope of the load versus strain difference plot exceeded a

predetermined value. A value of 10% slope change was

used in this study. This value was the ‘lowest’ value that

could confidently be used to identify buckling that was

not adversely influenced by the ‘noise’ of the strain data

obtained from the experiments. A typical plot of the

change of slope versus load is shown in Figure 3.

Average values of the estimated and the initial buck-

ling loads for the three types of beams tested are given

in Tuble 1. From the data in Tuble 1 it can be seen that

the percentage difference between the initial buckling

loads and the estimated buckling loads is 22%, 33% and

27% for beams V 3/X, P 318 and V l/2, respectively.

Photographs (taken during the testing) of the post-

buckled deformation (for example Figure 2) show

between three and four buckle half-wavelengths in the

In the estimation method the buckling load is deter-

mined graphically (or numerically) from the ‘knee’ in

the difference strain versus the load plot. The locationof the knee is determined by extending the initial linear Figure 2 Post-buckled deformation of a pultruded beam

120 I I I I 1 I I I r110 -

100 -

90 - estimated buckling______________--___~_-----~__‘--_________---------~

5

60 -

70

_.m- ’initial buckling

60-0d 50

- -f--------------------------------------------------------:

s 40 Pa- 1

30 . s-s3

20

f10

0’ ’ 1 I I I 1 1 I I

0 100 200 300 400 500 600 700 60 0 900 1000

Microstrain

201

-20 ’ / / 1 I I ! I I

0 10 20 30 40 50 60 70 60 90

Load (kN)

Figure 1 Load YL’~SUStrain difference plot Figure 3 Change of slope VP~SU.Soad plot

7 1

/10 0

326 Construction and Building Materials 1995 Volume 9 Number 6




Table 1 Experimental loads and stresses

Beam Initial buckling Estimated buckling Ultimate failure Initial buckling Estimated buckling

load, P,, load, P,,, load, P,,, stress, 4, stress, cr,,,

CkN) (W (kN WPa) WPa)

v 3/8 71.1 87.3 98.3 66.6 121.0P 318 66.9 89.0 96.1 62.6 123.1v II2 140.1 177.9 189.4 102.7 192.5

constant moment region of the beams. It is felt that the

lower ‘initial’ buckling load realistically represents the

onset of ‘elastic’ buckling, while the ‘estimated’ buck-

ling load is that which exists when the section has been

loaded into the irreversible post-buckled regime (see the

large post-buckled flange deformation shown in Figure

2). Loading, unloading and reloading tests show that

the buckling load is significantly reduced when the

beam is reloaded after having been loaded into the post-

buckled regime2. It can therefore be concluded that the

nonlinearity seen in the expermental data is caused byboth material nonlinearity due to accumulating mater-

ial damage and geometric nonlinearity. Although the

pultruded beams may appear to be undamaged follow-

ing unloading after an excursion into the post-buckled

regime, this is not the case, and designers are cautioned

against utilizing the post-buckling capacity. Although

deflection limits will usually govern beam design in

typical applications it is nevertheless vital to understand

the phenomenon of local buckling in pultruded beams

so that design codes can be developed for pultruded

structures. Based on the above, it is recommended that

the appropriate method for determining buckling loadsfrom strain data of this type be the ‘analytical’ method

and not the ‘estimation’ method. A simplified graphical

version of this method can also be used whereby the

buckling load is determined approximately by observing

where the onset of nonlinearity in the initial linear por-

tion of the load-strain difference plot occurs. For com-

parison purposes the average ultimate failure loads of

the beams are also shown in Tuble 1. Since the beams

fail in a number of different modes2s3 it is not possible

to directly compare the buckling loads to ultimate loads

for the purposes of safety factor estimation; however, it

is important to note that the ‘estimated’ buckling loads

are very close to the ultimate loads in all cases. Con-sequently, design approaches based on the ‘estimated’

buckling loads will have lower margins of safety and

should be avoided.

Following determination of the buckling loads a pro-

cedure is required to obtain the buckling stresses. Based

on experimental data in which it has been observed that

the distribution of axial strain across the compression

flange is nearly uniform’, the classical beam flexure for-

mula is used, vi z. CJ = o,,, = MC/Z , where cr,,,, is the

maximum flange compressive stress (shown throughout

this paper with a positive value for ease of presenta-

tion), M is the bending moment at the section, c is thedistance from the neutral axis to the compression face

in the elastic section, and Z is the second moment of

area of the elastic section. However, since a post-

buckled configuration exists at the ‘estimated’ buckling

load, a post-buckled version of the classical formula is

used in this case, viz. cr = My’lZ*, where y’ is the distance

to the face of the compression flange from the neutral

axis in the post-buckled section, and I* is the second

moment of area of the post-buckled section. The geom-

etry of the post-buckled section is obtained using an

‘effective width concept’ and experimental data for the

location of the post-buckled neutral axis’. For the four-

point-bend test geometry used M = Vu, where V = PI2

and c1 is the moment arm equal to 762 mm. The geo-

metric properties of beams V 318 and P 318 are I = 4.13

x 10’ mm4, I* = 3.24x 10’ mm4, c = 101.6 mm, y’ =

117.9 mm and for beams V l/2 are, I= 5.28 x 10’ mm’,

I* = 4.15 x 10’ mm4, c = 101.6 mm, y’ = 117.9 mm.

The calculated ‘initial’ and ‘estimated’ buckling

stresses are shown in Table 1. As can be seen from

Tuble I the ‘estimated’ stresses are significantly higher

than the ‘initial’ stresses. As mentioned previously the

‘initial’ stresses should be considered to be the ‘actual’

buckling stresses for the pultruded beams, while the

‘estimated’ buckling stresses give a measure of the

flange stress in the post-buckled configuration close to

failure of the beam. Therefore, while the initial bucklingstresses may be predicted using linear elastic analysis,

prediction of the ‘estimated’ buckling stresses will

require geometrically and materially nonlinear analysis.

Anistropy

In order to determine whether or not the experimental

‘initial’ buckling loads could be predicted from knowl-

edge of the section geometry and material properties an

analytical study was first conducted. Classical linear

elastic orthotropic plate buckling analysis” was per-

formed in which the compression flange was modelledas an orthotropic plate free on its longitudinal outer

edge and elastically restrained at its longitudinal inner

edge. This approach was chosen, as opposed to the

approach in which the buckling of the full-section is

modelled”, since it enables one to obtain a numerical

estimate of the extent of the web/flange interaction

through the edge restraint coefficient”.

The classical solution for an orthotropic plate which

is simply supported on its loaded edges is well docu-

mented’3a’4 and will not be repeated in detail. The solu-

tion is given in terms of the four in-plane independent

elastic constants of the orthotropic plate, E,,, E12, G,,,

v,~, the nondimensional buckling coefficient, K, =

N,b2/tiD,, the nondimensional edge restraint coefficient,

R = SblD,, the mode number, m, and the plate aspect

ratio, $ = u/b. N, is the in-plane load per unit width, b





is the plate width, D2 = &t3/{ 12(1 - vlzv,,)} is the plate

transverse rigidity, S is the restraining moment along

the rotationally restrained edge per unit length per unit

rotation” and a is the plate length. The buckling stress

is obtained as, CT=NJt, where t is the plate thickness.

The classical solution is obtained via the Levy solution

technique and results in a nonlinear transcendental

equation which is solved numerically. Typical results

are shown in Figure 4, which shows the dependence of

the buckling coefficient on the aspect ratio and the edge

restraint coefficient. For the beams tested in the experi-

mental study2-4 4 = 12.

In order to perform the above calculations the in-

plane material properties of the pultruded plate mater-

ial are needed. Results presented in this paper are given

for two different sets of material properties: those based

on properties provided by the manufacturer” of the

pultruded sections and identified as ‘design data’ and

those based on properties obtained from coupon testsconducted at the Georgia Institute of Technology16 and

called ‘Georgia data’. The two sets of data are given in

Table 2. As can be seen from Table 2, these two sets of

data are different. This is not uncommon and stems

E =24.6GPa E =10.27GPaG:;=3.66GPa v:~=O.333

0.0 1 I I I I I 1

0 2 4 6 a 10 12 1 4

Length-width Ratio # (a/b)

Figure 4 Buckling curve for elastically restrained orthotropic plate

Table 2 Material property data

PropertyVinylester (V 318, V 112) Polyester (P 318)

Design data Georgia data Design data Georgia data

-%, (GPa) 17.0 24.6 17.0 24.0

J% (GPa) 8.0 10.3 7.0 1.5Gr2 (GPa) 2.5” 3.7 2.0 2.6

“12 0.3” 0.33 0.34 0.31

“Data not provided by manufacturer and obtained from other sources3

from the fact that manufacturer data is given for design

purposes and is generally conservative. Recent results”

have indicated that the inhomogeneity of pultruded

materials, which is due to the manufacturing process,

can lead to significant differences in property data

depending on coupon size and location within the

section.

As can be seen from the buckling curve shown in

Figure 4, prediction of the buckling stress depends onthe value of R, the edge restraint coefficient. The buck-

ling stress for the two limiting cases of a simply-sup-

ported edge (R = 0) and a clamped edge (R = -) can,

however, be obtained. Comparison between the experi-

mental buckling stresses and the limiting cases is shown

in Table 3 for the different beams and material property

data. From Table 3 it can be seen that the expermental

buckling stress falls between the two limiting cases. For

design purposes the assumption of a simply-supported

edge is a conservative assumption. Since stability will

often dictate the design of pultruded structures it may

be desired to take account of the edge restraint provided

by the web/flange intersection to increase the design

load on the beam. In order to obtain the value of the

edge restraint coefficient from the experimental data the

buckling curves can be plotted in an alternative form as

shown in Figure 5. From plots such as these the value

of the edge restraint coefficient and the number of

buckle half-wavelengths (mode number) can be

obtained from the experimentally determined buckling

stress. In Figure 5 the specific case of a V l/2 beam is

shown. From the experimentally determined buckling

stress of 102.7 MPa (see Table I) an edge restraint coef-

ficient of 1.06 is obtained. In addition, it can be seen

that the analytical solution predicts four buckle half-wavelengths (m = 4) which agrees with the expermental

Table 3 Comparison between theoretical and experimental buckling stresses

$=12,t=9.5mm @= 12, I = 12.7 mm

%Wrlmrnl %WUnrnl

(MPa) (MPa)

R=O R=m R=O R=cm

Georgia data Vinylester 36.8 146.4 260.3

Polyester 26.8 114.2 62.2 47.6 203.0 NA

Design data Vinylester 102.7

Polyester 20.7 93.4 62.2 38.0 171.7 NA




2 5 0

2 2 5

2 0 0

3

$ ? 1 7 5

b-

In=8

wn=5 Vi n y l e s t e r

2 1 0 2 . 6

2 1 0 0

Lz

7 5

2 5

Design dataE,,=17.00GPa

E,,=8.00GPa

G,z=2.48GPa

” =0.3

a b=12b=95.25mmt=12.7mm

I-1

1

1 0 - l l o o 1 0 ' l o 2 l OA

Coefficient of Restraint R

Figure 5 Buckling curve used for determination of the edge restraintcoefficient

observations. Predictions of the edge restraint co-

efficient, R, and the mode number, m, for the beams

tested are given in Tuble 4. Experimental mode numbers

between 3 and 4 were obtained for all beams tested2s3.

The fact that the predictions with the design data show

mode numbers of 5 for the V 3/8 and P 3/8 beams sug-

gests that the design data are in fact lower than the true

material data. However, since the photographs of the

buckled deformation were taken in the post-buckled

range it is possible that the wavelengths may haveincreased (hence the decrease in mode number) from

those at the initiation of buckling due to damage of the

web/flange junction.

A parametric study was conducted to study the influ-

ence of the orthotropic material properties and the edge

restraint coefficient on the buckling behaviour. Figure 6

shows the value of the buckling stress as a function of

the variation in individual properties. The effect of rela-

tive changes in properties from the baseline properties

defined by the Georgia data (identified with superscript

‘0’) are shown. As can be seen from the figure the in-

plane shear modulus has the greatest effect on the buck-

ling stress. The effect of the edge restraint coefficientcan also be seen. The edge restraint coefficient can be

increased by increasing the size of the fillet region

between the web and the flange. It has been shown

Table 4 Analytical predictions of edge restraint coefficient and mode

number

t Gpcrrment m R

(mm) W’a)

9.5 66.6 3 0.75

Georgia Vinylester 12.7 102.7 3 0.19data

Polyester 9.5 62.6 4 I 06

Design Vinylester

data -~

Polyester

9.5 66.6 5 2.18

12.7 102.7 4 I .06

9.5 62.6 5 2.81


experimentally3 that such ‘customizing’ of the fillet

region significantly increases the buckling stress in pul-

truded beams.

Inhomogeneity

Composite materials are by definition inhomogeneous,

consisting of fibres in a surrounding matrix. Theoretical

analysis of composite materials on the macroscale is

based on the assumption of ‘statistical homogeneity’ in

a ‘representative volume element’ and the theory of

laminated plates. For composite materials made by pre-

cise lay up of prepregs these two assumptions appear to

be valid. However, for pultruded composite materials,

these assumptions cannot be made. Inspection of a

through-the-thickness section of a pultruded material

shows inhomogeneity on the scale of the part itself, con-

sisting of clusters of roving reinforcements in ‘arbitrary’

locations both in and out of the plane of the material”.Although some layering due to the presence of continu-

ous stand mats does exist it is not precise as in the case

of a laid-up composite plate. This is due to the nature

of the pultrusion process which has only approximate

control over the placement of reinforcements (fibres,

mats and fabrics) entering the die and no control during

the curing processes within the die. In particular,

inspection of a profile section shows that the reinforce-

ments tend to be most ‘arbitrary’ at the free edges and

at the junctions between plates. Often the region near a

free edge (up to 10 mm) may have fewer roving bundles

than the rest of the plate, while the reinforcement matsin the region of the junctions may be folded over in a

bunched fashion. Therefore test coupons are not taken

from these regions and their properties are ‘unknown’.

However, it can be assumed that the properties of these

sections are lower than the average properties of the

pultruded material in the flat parts of the profile. It has

1 . 2 0

1 . 2 5

1 . 2 0

1 . 1 5

Ob X

A, 1 1 0

b

0 1 . 0 5

3

l + z 1 . 0 0

iil 0.95

v) 0.90

2_9

0.85

S 0 8 0

a l

0 . 7 5

0 7 0 -J

0 . 5 0 6 0 . 7 0 . 8 0 . 9 1 . 0 1 . 1 1 . 2 1 . 3 1 . 4 1 . 5

Va n a b l e Ratio (EI1/EP,, E,,/Eiz, GI , / G , l , s / s ' )

Figure 6 Parametric representation of buckling stress





additionally been shown I7 that even in the flat parts of

the section variations in stiffness properties may be as

much as 65% depending on location in the cross-section.

In order to account for the influence of the inhomo-

geneity on the local buckling behaviour of the pultruded

beam an elastic buckling analysis using the COSMOS

finite element code was performed. The finite element

method was chosen since it permits the user to vary the

material properties throughout the cross-section in an

arbitrary manner and also allows for precise modelling

of the beam support and loading conditions. Analytical

studies of in-plane inhomogeneous composite plates

are few and have considered only simplified distribu-

tions of the in-plane properties, primarily for theoretical

purposes’8*‘9.

The beams were modelled using anisotropic plate ele-

ments measuring 25.4 mm by 25.4 mm. Each cross-sec-

tion was divided into 24 elements. Lengthwise the 3048

mm long beam was divided into 120 elements giving atotal of 2880 elements in the beam model. To investi-

gate the effect of plate inhomogeneity different distribu-

tions of in-plane properties were chosen. The property

distributions chosen for the inhomogeneous cases are

shown in Figure 7. The distributions were chosen in an

attempt to account for lower properties at the edges and

the intersections and to investigate the influence of the

longitudinal properties versus the transverse properties.

They were refined by a trial-and-error method for pur-

poses of demonstrating the dependence of the buckling

load on material inhomogeneity. In all the distributions

shown in Figure 7 a constraint condition was chosen

such that the average property over the plate was equal

in value to the Georgia data. A baseline case in which

the average property was used throughout the cross-sec-

tion (uniform case) was used for comparison purposes.

Models were run in which either all or selected material

properties were varied while the remaining properties

were held uniform. In one model only the longitudinal

modulus, E,,, was varied according to the distributions

shown in Figure 7, while in the other case the transverse

and Poisson properties were varied while the longitudi-

nal modulus was held uniform. Such ‘arbitrary’ choices

of property variations are theoretically possible since allfour constants are independent; however, in reality it is

likely that there would be a relationship between these

properties due to the microstructure of the material.

Results of the finite element analyses are given in

Table 5. A number of interesting features can be seen in

I8

I I

Figure 7 Distribution of properties in the beam cross-sections

Gz#e2 Case 3

Table 5 Buckling loads (kN) of beams with variable material properties

V 318 P 3/8 v 112

Experimental buckling load71.1 69.9

FEM analysis buckling load (uniform properties)

88 70 I

FEM analysis buckling load (variable properties)

Case 1 70.0 80.0 67.7 47.7 156.6Case 2 62.0 89.0 70.0 56.2 141.5Case 3 69.0 84.6 16.2 59.5 160.0




these results. The assumption of uniform properties

throughout the cross-section leads to FEM predictions

which are greater than the experimental loads. The FEMpredictions in which variable properties are used can be

very close to the experimental values (this, of course,

depends on the distributions chosen in Figure 7). The

influence of the transverse property variations is much

more significant than of the longitudinal property vari-

ation. In fact, the low predicted values of the P 318

beam in contrast to the V 3/8 beams (all properties

varied) is almost entirely a function of the transverse

property variation since the longitudinal modulus of

these beams is very similar (see Table 2). The results

suggest that material inhomogeneity should be included

in finite element analyses of pultruded beams, and that

variation of the properties in the edges and junctions of

the beams can have a significant effect on the overall

performance of pultruded beams. It remains to be deter-

mined if the property variations chosen in this study are

indeed a true representation of the actual material

property variations

Conclusion

Prediction of the local buckling loads in pultruded fibre

reinforced plastic beams subjected to flexural loading is

influenced by a number of factors arising from the non-

linearity in expermental data and from the anisotropic

and inhomogeneous material properties of the beams.

It has been shown that nonlinear experimental data

obtained from full-scale tests on pultruded beams mustbe correctly interpreted so as not to overestimate the

buckling capacity of these beams. An argument has

been made for estimating buckling loads at the very

onset of nonlinearity in the test data, and not at the

point at which large and visible post-buckling deforma-

tion occurs. It has also been shown that the value of the

edge restraint coefficient for a pultruded beam can be

obtained from a combination of test data and classical

orthotropic plate theory. Parametric studies have been

presented which show that the in-plane shear modulus

has the largest influence on the buckling load. The

importance of utilizing the ‘actual’ material properties

in analytical or numerical studies has also been empha-

sized. It has been demonstrated that material inho-

mogeneity in pultruded beams can be a cause of

discrepancies between experimentally determined buck-

ling loads and those predicted by finite element meth-

ods. The assumption of uniform material properties

throughout the beam may not be appropriate for the

analysis of pultruded beams.


Acknowledgement

Support for this study was provided by the National

Science Foundation under grant number MSM-9015502

(Dr K. Chong, Program Director). The pultruded

beams used in the experimental study were provided by

Creative Pultrusions, Inc.

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I

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IO

I5

1617

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Local Buckling of Pultruded Beam(Bank LC)

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