This is the fifth column taken from my book Composites for Construction — Structural Design with FRP Materials (published by John Wiley & Sons Inc., New York, N.Y.). In this installment, I discuss the design basis for structures made with pultruded profiles. As most readers of this magazine know, pultrusion is a cost-effective continuous manufacturing process for producing fiber-reinforced polymer (FRP) structural profiles with constant cross-sections, such as I-, box-, channel- and angle-shaped sections. Truss structures and braced framed structures have been made for more than 30 years using pultruded members, particularly where corrosion resistance is required, as in food or chemical processing plants; where electromagnetic transparency is needed in electronics manufacturing; or where only lightweight materials can be transported into a construction site, such as for a footbridge in a park setting.
Pultruded profiles are typically made with glass fiber reinforcement and thermosetting resins, that is, polyester, vinyl ester or epoxy. Considered by engineers as thin-walled laminated plates, these profiles normally have continuous reinforcing rovings running longitudinally with continuous strand mat (CSM) for transverse strength (customized pultrusions can include bidirectional fabrics to improve mechanical properties). Fiber volume fraction is typically 30 to 50 percent.
Conventional FRP profiles are produced in profile shapes that mimic metallic versions. Unlike aluminum or steel profiles, there are no shared standard geometries or mechanical and physical property standards for FRP pultrusions in the U.S. at the present time. Each pultruder, however, does provide literature that specifies each profile’s geometry and properties (major pultruders are listed in “Companies”, at left). Further, and unlike the composite engineering materials covered in my previous columns, there also are no universally accepted guidelines for the design of framed structures using conventional or custom pultruded profiles. There do exist, however, two general design manuals for structural engineers: the Structural Plastics Design Manual (ASCE, 1984) and the Eurocomp Design Code and Handbook (Eurocomp, 1996). While the evidence is sufficient to confirm that the analytical equations in these two references are suitable for use in designing structures with profiles, there is little consensus about what safety and resistance factors to use. Although Bedford Reinforced Plastics, Creative Pultrusions Inc., Strongwell and Fiberline Composites A/S (see “Learn More”) offer the most comprehensive in-house design manuals, each is intended for use only with that company’s profile products.
Two Design Bases
Most standard profiles are constructed of flanges and webs of orthotropic thin plates, in which the laminate is assumed to be both balanced and symmetrical. Specific notations are used to identify constants, stresses and strains in such plates: in-plane directions are identified as the longitudinal (L), transverse (T) and shear (LT) directions. The out-of-plane direction is referred to as the through-the-thickness direction (TT). Thus, for example, the in-plane stiffness constant is EL and the longitudinal modulus is ET. Note that in manufacturers’ in-house design guides, the longitudinal direction is sometimes referred to as the machine or pultrusion direction and designated lengthwise (LW), while the transverse direction may be called the crosswise (CW) direction.
The European Standard EN 13706 (CEN 2002) is currently the only published standards document that specifies minimum properties for var-ious grades of pultruded materials. These minimums, with the grade name (E17 or E23) taken from the minimum longitudinal tensile modulus of that grade, are shown in Table 1 along with the tests required for obtaining them. In the U.S., ASTM International (W. Conshohocken, Pa.) has recently published its D 7290 “Standard Practice for Evaluating Material Property Characteristic Values for Polymeric Composites for Civil Engineering Structural Applications,” which can be used to determine the characteristic properties of pultruded composites materials for use in design codes. This, however, is not a specification because it does not specify minimum properties for the different classes or grades of pultruded materials.
For design purposes, it is generally assumed that pultruded materials behave in a linear elastic manner in tension, compression and shear, in both the longitudinal and transverse directions, and that failure is brittle. These are reasonable assumptions at the strain levels typical of service loads — about 20 percent of ultimate — but not true at high strain, where stress/strain behavior has been found to be highly nonlinear and failure may be progressive. Because the design of most pultruded profiles is normally controlled by deflection, and because large factors of safety are used, service stress rarely exceeds the 20 percent level.
It is a professional requirement for a structural engineer to declare the design basis of a structure clearly and unambiguously, which is never a problem for traditional materials like steel and concrete. However, as noted above, in the absence of a consensus-based design basis for pultruded members, the engineer must document his/her assumptions — not a routine task in this case. In my book, I’ve suggested two different design bases: one is an allowable stress design (ASD); the second is a load and resistance factor design (LRFD).
Under ASD, no structural member reaches its ultimate strength under no-minal service loads. Thus, the allowable stress (σallow) is the material’s ultimate strength (σult) divided by the factor of safety, SF. The nominal service loads are obtained from building codes or model load codes (such as ASCE 7-05). This approach is recommended by most U.S. pultrusion companies; typical safety factors are presented in Table 2. These SFs are used with the analytical or empirical equations provided in manufacturers’ design guides, which have been developed based on testing conducted by that company. It should be noted that the ASD approach does not provide a known degree of structural reliability because it is not known with a quantifiable degree of confidence what the probability is that the structure will be able to withstand the design loads in various limit states. This is because simple tests form the basis of the SFs, without statistical data that establish the degree of variability in material properties. However, the values provided are conservative, and assumed loads and forces come from probabilistically based codes.
In contrast, LRFD used in the U.S. and the closely related limit states design (LSD) basis used in Europe are based on the belief that the level of safety or serviceability of a design must produce a quantifiable level of structural reliability. Nominal loads, P, are factored by probabilistically derived load factors, γ, which depend on load type and load combinations; the material or structural nominal resistances are factored by resistance factors, φ, that depend on material variability and type of failure. The required member resistance Rreqd is determined using elastic or inelastic analytical methods as a function of the factored loads. A reliability index, β, is used to quantify structural reliability in probability-based design. Where well-established analytical methods exist for the prediction of deformation and failure, as is the case for steel and concrete, lower ranges of β are accepted, but for composite pultruded members, higher values of β — from 3.0 to 4.5 — are used. While no LRFD exists for pultruded materials, a prestandard outline has been prepared by ASCE (Chambers, 1997) and a discussion of design issues is presented in Ellingwood (2003). The LRFD approach is hampered by the fact that manufacturers don’t follow one standard material specification that, in an ideal world, would be accompanied by a large database of statistically based material properties.
A third avenue, performance-based design, also exists. In this approach, the structural design of an FRP pultruded member structure can be based on a specific performance specification, as established in Performance Code for Buildings and Facilities by the International Code Council (Falls Church, Va.). The entire structure or a designated portion has to meet structural performance objectives that are set out in advance and documented with full-scale failure testing. The performance specifications are usually appended to the project’s construction documents as “special provisions” and are not uncommon in the composites industry. Whatever design basis is used, it is important that the factor of safety or the structural reliability index be defined and agreed upon in advance by the designer and owner/client as part of the project contract.
Going forward, I anticipate that pultruded profile manufacturers will follow a standard material specification, such as European Standard EN 13706 (2002), or will develop one based on proposed model specifications, such as the one that I have proposed in Bank, et al. (2003). In the long term, a design standard for pultruded structures, similar to those used for other materials is needed if use of pultruded structures is to increase. Fortunately, such an effort was recently initiated by the American Composites Manufacturers Assn. (ACMA) and the American Society of Civil Engineers (ASCE). A standard will be available in the U.S. in the next three to five years.
Excerpt published with permission from John Wiley & Sons. Composites for Construction — Structural Design with FRP Materials is available for $135 (USD) at www.wiley.com or from www.bn.com, www.amazon.com or www.borders.com.
References:
- ASCE, 1984, Structural Plastics Design Manual, ASCE Manuals and Reports on Engineering Practice 63, American Society of Civil Engineers, Reston, Va.
- ASCE, 2005, “Minimum Design Loads for Buildings and Other Structures,” ASCE 7-05, American Society of Civil Engineers, Reston, Va.
- Bank, L.C., Gentry, T.R., Thompson B.P., and Russell, J.S., 2003, “A Model Specification for FRP Composites for Civil Engineering Structures,” Construction and Building Materials, Vol. 17, No. 6-7, pp. 405-437.
- Chambers, R.E., 1997, “ASCE Design Standard for Pultruded Fiber-Reinforced Plastic (FRP) Structures,” Journal of Composites for Construction, Vol. 1, pp. 26-38.
- Ellingwood, B.R., 2003, “Toward Load and Resistance Factor Design for Fiber-Reinforced Polymer Composite Structures,” Journal of Structural Engineering, Vol. 129, pp. 449-458.
- Eurocomp, 1996, “Structural Design of Polymer Composites,” Eurocomp Design Code and Handbook (J. Clarke, ed.), E&FN Spon, London.