Applied Mechanics and Materials Vols. 105-107 (2012) pp 1671-1676 Online available since 2011/Sep/27 at www.scientific.net © (2012) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMM.105-107.1671
Experimental Evaluation on Fixed End Supported PFRP Channel Beams and LRFD Approach Jaksada Thumrongvut 1,a and Sittichai Seangatith 2,b 1,2
School of Civil Engineering, Suranaree University of Technology, Nakhon Ratchasima, 30000 Thailand. a
b
[email protected],
[email protected]
Keywords: Pultruded fiber reinforced plastic, Channel profile, Flexural-torsional buckling, Fixed End Supported, LRFD Approach.
Abstract. In this paper, the experimental results on the fixed end supported PFRP channel beams subjected to three-point loading are presented. The aims of this study are to evaluate the effects of the span ( L) on the structural behaviors, the critical buckling moments and the modes of failure of the beams, and to compare the obtained critical buckling moments with those obtained from the modified LFRD steel design equation in order to check the adequacy of the equation. The beam specimens have the cross-sectional dimensions of 76 × 22 × 6 mm, with span-to-depth ratio ( L / d ) ranging from 13 to 52. A total of twenty-six specimens were tested. Based on the experimental results, it was found that the loads versus mid-span vertical deflection relationships of the beams are linear up to the failure. On the contrary, the load versus mid-span lateral deflection relationships are geometrically nonlinear. The general modes of failure are the flexural-torsional buckling. Finally, the modified LFRD equation can satisfactorily predict the critical buckling moment for L / d exceeds 20. However, for L / d < 20, the equation overestimates the critical buckling moment of the beams and more development is needed. Introduction Fiber-reinforced plastic (FRP) composite materials are widely used in civil engineering applications, especially in two main functions: in rehabilitating or reinforcing, and in new structures [1]. The FRP composite is a material composed of fiber reinforcement bonded to a polymer resin or matrix (e.g., polyester, vinylester and epoxy) with distinct interfaces between them. In the form of FRP, the fibers and polymer resins still have their own physical and chemical properties. The fibers provide strength and stiffness, and resins provide shape and protect the fibers from damage. Among various types of manufacturing processes, the pultrusion process appears to offer the highest productivity-to-cost ratio. The FRP manufactured by this process is called pultruded fiber reinforced plastic (PFRP). Over the past two decades, the usages of the PFRP structural profiles have been significantly increased into the civil engineering constructions due to the material characteristics and economic advantages over the conventional materials such as steel and reinforced concrete. The advantages include high corrosion resistance, high strength-to-weight ratio and ease of installation [2]. However, due to the relatively low stiffness and sectional geometry of PFRP shapes, the problems with global instability and large deformations are common in the structural shapes. Mostly, their design is governed by the serviceability parameters such as large deflection or buckling instability, depending on the geometry of the cross-section, the material properties, and the loading conditions [3]. In addition, the critical obstacles to their widespread applications in construction are the lack of simplified and reliable design criteria [4]. The research and development of all PFRP structures in civil engineering have progressed considerably in several countries. Numerous experimental and theoretical investigations have been performed regarding the PFRP structural members subjected to flexure. Indeed, most of them have All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP, www.ttp.net. (ID: 202.28.41.1-29/09/11,09:34:43)
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emphasized on the lateral buckling behavior of the members for doubly symmetric cross-sections such as wide-flange, I, and box profiles. Only few research works on mono-symmetric channel profiles were carried-out [5]. In recent years, the applications of the structural profile, especially the channel profile, have been increased considerably in variety of secondary structures and structural components such as purlins, trusses and bracing members. Also, in order to create further confidence in the application of the profile, it is necessary to enhance knowledge of its structural performance, especially the global behaviors and the global instability. This paper is intended to satisfy a portion of that need. Therefore, the objectives of this paper are to present the experimental results on the behaviors and mode of failure of the fixed end supported PFRP channel beams under three-point loading and to compare the obtained critical buckling moments with those obtained from the modified LRFD steel design equation [6] in order to check the adequacy of the equation. Test Specimens and Experimental Procedures The PFRP channel members used in this study were made of E-glass fiber reinforced polyester resin, and manufactured by a pultrusion process. They have the cross-sectional dimensions of 76 × 22 × 6 mm with span-to-depth ratio ( L / d ) ranging from 13 to 52. A total of twenty-six specimens were tested. Two tests were performed on each span-to-depth ratio. Details of the test profiles, dimensions, and geometric properties are presented in Table 1. The specimen numbers were designated in the form of "Cd − F − L " . For example, the specimen number C76-F-2.5 is the PFRP channel specimens, having depth (d ) of 76 mm, F (fixed end supported), and span ( L ) of 2.5 m, respectively. Table 1. Geometric properties of the pultruded FRP channel specimens Specimens C76-F-1.0 C76-F-1.2 C76-F-1.5 C76-F-1.7 C76-F-2.0 C76-F-2.2 C76-F-2.5 C76-F-2.7 C76-F-3.0 C76-F-3.2 C76-F-3.5 C76-F-3.7 C76-F-4.0
( d × b × t ) [mm] 76 × 22 × 6 76 × 22 × 6 76 × 22 × 6 76 × 22 × 6 76 × 22 × 6 76 × 22 × 6 76 × 22 × 6 76 × 22 × 6 76 × 22 × 6 76 × 22 × 6 76 × 22 × 6 76 × 22 × 6 76 × 22 × 6
L [m] 1.0 1.2 1.5 1.7 2.0 2.2 2.5 2.7 3.0 3.2 3.5 3.7 4.0
L/d 13.2 15.8 19.7 22.4 26.3 28.9 32.9 35.5 39.5 42.1 46.1 48.7 52.6
4
I y [mm ] 21812 21812 21812 21812 21812 21812 21812 21812 21812 21812 21812 21812 21812
4
J [mm ] 8208 8208 8208 8208 8208 8208 8208 8208 8208 8208 8208 8208 8208
6
Cw [mm ] 7
2.660 × 10 2.660 × 107 2.660 × 107 2.660 × 107 2.660 × 107 2.660 × 107 2.660 × 107 2.660 × 107 2.660 × 107 2.660 × 107 2.660 × 107 2.660 × 107 2.660 × 107
Number 2 2 2 2 2 2 2 2 2 2 2 2 2
To correlate the analytical results with the obtained test results, the values of the longitudinal modulus ( EL ) and the in-plane shear modulus (GLT ) were determined from the tension test in accordance with ASTM D3039 and the in-plane shear coupon test in accordance with ASTM D5379, respectively. This shear coupon test is in the form of V-notched beam test with the pure shear under a four-point asymmetric bending configuration. From the coupon tests, it was found that the average values of EL and GLT were 35.20 GPa and 2.18 GPa, respectively. In addition, the results from the distributed analysis of all the mechanical properties were in good agreement with the values of the coefficient of determination (COD) which is close to 1.0. The typical test set-up configuration for the fixed end supported with three-point loading test of the PFRP beam specimen is shown in Fig. 1. The both fixed ends were set-up by using wood clamps. It is very important to ensure that the clamp was properly tightened. In this way, the both wood clamps were firmly gripped with the rigid supports. At the mid-span, a bolt with M16 nut was
Applied Mechanics and Materials Vols. 105-107
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firmly installed on the neutral axis of the cross-section, so that the concentrated vertical load can be applied passing directly through the shear center of the cross-section in order to provide the applied loads to the beams without torsion. The loads were initially applied by sequentially adding steel pendulums on a loading platform. The incremental loads were added until reaching the critical buckling loads and the failure of the beams. It should be noted that the critical buckling load is the values of the corresponding highest end loads at which prior to failure of the beams. In addition, two 100 mm linear variable differential transducers (LVDTs) were used to measure the vertical and lateral deflection of the beams in mid-span section, as shown in Fig. 1(b). The overall deflections were automatically recorded by a MW100 YOKOGAWA data acquisition unit. Finally, the failure mechanisms were also recorded. Bolt M16
A
Channel profile Bolt M16 S
Wood clamp (Fixed end supported )
A
Rigid support
C
LVDT
Rigid support Vertical arm
L/2
LVDT
Vertical arm Pendulum
Pendulum Loading platform
Loading platform
(section A-A) L
(a) (b) Fig. 1 Test setup (a) A schematic view and (b) Load applied through the shear center Experimental Results and Discussions Behaviors and Modes of Failure. Fig. 2(a) and 2(b) demonstrate the behaviors of the PFRP beams in terms of applied load and mid-span vertical and lateral deflection, respectively. For the mid-span vertical deflection, it can be seen that the behavior of all beams have a linear elastic response up to 90-95% of the obtained critical buckling load. Afterwards, the curves are becoming nonlinear and leading to the buckling failure of the beam. From the tests also showed that the short span beam has a slightly higher degree of nonlinear response before failure than that of the longer span beam. This difference is probably due to the fact that the response of the longer span beams is less stiff than that of the shorter span beams. 6000
6000
Load (N)
4000
3000
C76-F-1.0(B)
C76-F-1.0(A)
C76-F-1.0(B)
C76-F-1.2(A)
C76-F-1.2(B)
C76-F-1.2(A)
C76-F-1.2(B)
C76-F-1.5(A)
C76-F-1.5(B)
C76-F-1.5(A)
C76-F-1.5(B)
C76-F-1.7(A)
C76-F-1.7(B)
C76-F-1.7(A)
C76-F-1.7(B)
C76-F-2.0(A)
C76-F-2.0(B)
C76-F-2.0(A)
C76-F-2.0(B)
C76-F-2.2(A)
C76-F-2.2(B)
C76-F-2.2(A)
C76-F-2.2(B)
C76-F-2.5(A)
C76-F-2.5(B)
C76-F-2.5(A)
C76-F-2.5(B)
C76-F-2.7(A)
C76-F-2.7(B)
C76-F-2.7(A)
C76-F-2.7(B)
C76-F-3.0(A)
C76-F-3.0(B)
C76-F-3.0(A)
C76-F-3.0(B)
C76-F-3.2(A)
C76-F-3.2(B)
C76-F-3.5(A)
C76-F-3.5(B)
C76-F-3.7(A)
C76-F-3.7(B)
C76-F-4.0(A)
C76-F-4.0(B)
5000
4000
Load (N)
5000
C76-F-1.0(A)
2000
1000
C76-F-3.2(A)
C76-F-3.2(B)
C76-F-3.5(A)
C76-F-3.5(B)
C76-F-3.7(A)
C76-F-3.7(B)
C76-F-4.0(A)
C76-F-4.0(B)
3000
2000
1000
0
0 0
1
2
3
4
5
6
7
8
9
10
Mid-span vertical deflection (mm)
11
12
13
14
15
0
5
10
15
20
25
30
35
Mid-span lateral deflection (mm)
(a) mid-span vertical deflection (b) mid-span lateral deflection Fig. 2 Load and mid-span deflection relationship of beams
40
45
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For the mid-span lateral deflection, the response curves show that the PFRP beams are in general similar to each other. The load versus mid-span lateral deflection relationships of the beams are geometrically nonlinear, and the response curves exhibit gradually increasing nonlinearity toward the buckling load. At the buckling load, all of specimens were failed in the form of twisting and large lateral displacement occurred simultaneously in the form of the flexural-torsional buckling mode of failure. No external material damage was observed. Fig. 3(a) to 3(c) show the failure modes of the pultruded FRP channel beams with span of 1.0, 2.0 and 3.0 m, respectively.
Fig. 3 Typical modes of failure (a) L = 1.0 m, (b) L = 2.0 m and (c) L = 3.0 m of PFRP channel beams with ratio L / d = 13.2, 26.3 and 39.5, respectively Critical Buckling Moment and Comparison with LRFD Approach. For the fixed end supported under three-point bending tests, the observed critical buckling load ( Pcr ) can be converting to the critical buckling moment ( M cr ) by using the equation: M cr = Pcr L / 8
(1)
It also should be noted that the equation (1) is acceptable for the beams with small deflection, having a linear behavior. The averaged critical buckling moment for each pair of the specimens is considered as the experimental critical buckling moment ( M cr ,EXP ) . Table 2 shows the experimentally obtained critical buckling moment ( M cr ,EXP ) of the beams. This indicates that the critical moment increases as the span of beam decreases. Also, the degree of flexural-torsional buckling of the channel beams in this study depends on the spans of the beams. With the increasing span, the flexural-torsional buckling mode is more noticeable. To predict the elastic buckling moment of steel channel specimens, the 1999 AISC/LRFD specifications give the equation in the form of [6]:
π
2
πE EI y GJ + (2) I y Cw L L where E is the modulus of elasticity, I y is the moment of inertia of the cross-sectional area about minor axis, G is the shear modulus of elasticity, J is the torsional constant, Cw is the warping constant and Cb is a modification factor for non-uniform moment diagrams. For moment diagrams along the member other than uniform moment and any supported, the buckling strength is obtained by multiplying the basic strength with Cb . Kirby and Nethercot [7] present an equation that applies to various shapes of moment diagrams within the unbraced segment in form of: M cr = Cb
Applied Mechanics and Materials Vols. 105-107
Cb =
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12.5M max 2.5M max + 3M A + 4 M B + 3M C
(3)
in which M max is the maximum moment, M A , M C are the moments at the quarter point and three quarter point, respectively, and M B is the moment at the mid-span of the beam. By using an equation (3), the values of the modification factor for the fixed end supported with three-point loading is equal to 1.92. Since the PFRP material is usually considered as orthotropic and homogeneous material, characterized by two independent elastic constants: the longitudinal tensile modulus of elasticity ( EL ) and in-plane shear modulus (GLT ) . Therefore, Equation (2) should be modified by using the elastic constants in place of the isotropic modulus of elasticity ( E ) and shear modulus of elasticity (G ) , respectively. Then, the modified expression for the critical buckling moment may be rewritten as:
M cr ,LRFD = Cb
2
π
πE EL I y GLT J + L I y Cw L L
(4)
Table 2. Experimental critical buckling moment and comparison with modified LRFD equation Specimens
C76-F-1.0 C76-F-1.2 C76-F-1.5 C76-F-1.7 C76-F-2.0 C76-F-2.2 C76-F-2.5 C76-F-2.7 C76-F-3.0 C76-F-3.2 C76-F-3.5 C76-F-3.7 C76-F-4.0
L/d 13.2 15.8 19.7 22.4 26.3 28.9 32.9 35.5 39.5 42.1 46.1 48.7 52.6
Test A
Experiment Test B
Averaged
Analytical LRFD M cr ,EXP
M cr ,A [N-m]
M cr ,B [N-m]
M cr ,EXP [N-m]
M cr ,LRFD [N-m]
M cr ,LRFD
657 579 481 422 362 331 284 257 238 215 205 192 176
645 551 446 401 350 318 269 241 212 207 183 172 161
651 565 464 412 356 324 277 249 225 211 194 182 168
871 687 523 452 376 338 294 271 242 226 206 195 180
0.75 0.82 0.89 0.91 0.95 0.96 0.94 0.92 0.93 0.93 0.94 0.93 0.94
Table 2 presents the obtained critical buckling moment compared with those ( M cr ,LRFD ) predicted by equation (4). The M cr ,EXP / M cr ,LRFD ratios are also presented to show the correlation between the experimental results and the predicted results. From the analytical results, the M cr ,EXP / M cr ,LRFD ratios are in the range of 0.75 to 0.96. For L / d > 20 , the M cr ,EXP / M cr ,LRFD ratios show the values close to unity, indicating that the experimental results are in good agreement with the predicted results. The deviation from unity may be primarily due to the unavoidable initial crookedness of the specimens. However, for L / d < 20 , the M cr ,EXP / M cr ,LRFD ratios are in the range of 0.75 to 0.89, indicating that the modified LRFD design equation overestimates the buckling moment of the PFRP channel beams by approximately 10-25%, depending on the span-to-depth ratio. This is due to the fact that the short beam has higher degree of nonlinear response before failure than the longer beam, which can be seen in Fig. 2(a). Fig. 4 shows the plots between the test results with the predicted results from the modified LRFD design equation in order to check the adequacy of the equation. It can be seen that the modified equation can not by accurately used to predict the critical buckling moment when the short beam with the span-to-depth ratio less than 20 and more development is needed.
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Critical Buckling Moment, Mcr (N-m)
1000 900
LRFD (Critical Buckling Moment)
800
Experiment
700 P
600 500 400 300 200 100 0 0
5
10
15
20
25
30
35
40
45
50
55
60
Span-to-depth ratio, L/d
Fig. 4 Critical buckling moment versus span-to-depth ratio Conclusions Based upon the results, the following conclusions can be drawn: 1.) The relationship between the load and mid-span vertical deflection of the PFRP channel beams are almost linear up to the failure. In contrast, the load versus mid-span lateral deflection relationships are geometric nonlinear response and the response curves exhibit gradually increasing nonlinearity toward the buckling failure of the beam. All of specimens were failed in the form of twisting and large lateral displacement occurred simultaneously in the form of the flexural-torsional buckling mode of failure. 2.) By comparing the obtained critical buckling moment with those predicted by the modified LRFD steel design equation, for L / d > 20 , it was found that they are in good agreement. However, the orthotropic effect of the pultruded material with a EL / GLT ratio of 16.1 does play an important role on the critical buckling moment for the short beam with L / d < 20 and more development is needed. Acknowledgments The authors gratefully acknowledge all the supports of Suranaree University of Technology for this study, which is a part of the research project “The Development of Design Equation for PultrudedFiber Reinforced Plastic Having C-Section under Compression and Flexure”.
References [1] [2] [3] [4] [5] [6] [7]
G. Promis, A. Gabor, G. Maddaluno and P. Hamelin: Composite Structures Vol. 92 (2010), p. 2565 R.J. Brooks and G.J. Turvey: Composite Structures Vol. 32(1-4) (1995), p. 203 N.I. Kim, D.K. Shin and M.Y. Kim: Engineering Structures Vol. 29 (2007), p. 1739 J. Thumrongvut and S. Seangatith: Key Engineering Materials Vol. 471-472 (2011), p. 578 L.Y. Shan and P.Z. Qiao: Composite Structures Vol. 68(2) (2005), p. 211 AISC: LRFD Specification for Structural Steel Buildings. (AISC, USA 1999) P.A. Kirby and D.A. Nethercot: Design for Structural Stability. (John Wiley and Sons 1979)
Vibration, Structural Engineering and Measurement I doi:10.4028/www.scientific.net/AMM.105-107 Experimental Evaluation on Fixed End Supported PFRP Channel Beams and LRFD Approach doi:10.4028/www.scientific.net/AMM.105-107.1671
