## 1613 Design Basis for Pultruded Structures

A basis for design of FRP pultruded structures is needed. In the absence of an approved design code for FRP pultruded structures a design basis must be agreed upon by all parties (owner, designer, contractor, and local authorities). Four types of design basis approaches are typically used for FRP pultruded structures:

1. Allowable-stress design (ASD).

2. Limit states design (LSD).

3. Load and resistance factor design (LRFD).

4. Performance-based design (PBD).

### 16.1.3.1 Allowable-Stress Design

ASD requires that the calculated design stresses (the required demand, oreqd) obtained from nominal service loads be less than the ultimate strengths (the capacity, out) divided by an appropriate factor of safety (SF). The ultimate strength divided by the safety factor is termed the allowable stress (ffaUow). Safety factors have traditionally been determined from industry practice and are not based on probabilistic methods. They do not provide a measurable reliability index

ASD is recommended by most pultrusion companies (e.g., Creative Pultrusions 2000; Strongwell 2002) in their design manuals. For ASD the safety factors typically recommended by pultrusion companies for their common structural shapes are

Flexural members (beams) = 2.5

Compression members (columns) = 3.0

Shear

Connections

These factors are applied to strength and stability. For deformation calculations the safety factors recommended are

Longitudinal and transverse moduli = 1.0 Shear moduli = 1.0

These factors are applied to the material properties and design equations provided in the company literature. These design equations are often empirically derived from test data. Material properties are provided in the company literature for different grades of pultruded material. Designs are based on unfactored nominal service loads.

ASD is also recommended by AASHTO (2001) in the Standard Specifications for Structural Supports for Highway Signs, Luminaires and Traffic Signals. The design equations provided in this specification are based on theoretical equations for orthotropic plates, beams, and columns of linear elastic materials made of glass reinforced polyester. Structural members may be manufactured by pultrusion, centrifugal casting, or filament winding. The following minimum safety factors are recommended:

Bending strength = 2.5 Tensile strength = 2.0 Compressive strength = 3.0 Shear strength = 3.0

Material properties to be used in the design equations are obtained from American Standard for Testing and Materials (ASTM) standard test methods. Designs are based on loads provided in the American Association for State Highway and Transportation Officials (AASHTO) specification. Full-scale testing according to ASTM 4923 is provided as a PBD method as an alternative to the analytical design. Where the analytical ASD method is used ''design calculations provided shall be verified by documented test results on similar structures.'' (AASHTO 2001, p. 8-5).

ASD is also commonly used by structural designers in conjunction with design equations based on theoretical equations for orthotropic plates, beams, and columns. Equations provided in the SPDM (1984) are typically used in calculations. Material properties are often obtained from standard ASTM tests. Minimum properties are usually specified in a design basis document (often referred to as a ''Special Provision to the Specifications''). Safety factors recommended by the pultrusion companies are usually used in this approach. Designs are based on unfactored nominal service loads.

### 16.1.3.2 Limit States Design

LSD requires that the design requirement (or actions) of the loads be less than the design resistance (or capacity) of the structure or structural members. The design loads and capacity are both multiplied by appropriate factors. The two primary limit states considered are the ultimate limit state (ULS) and the serviceability limit state (SLS). The ULS is associated with collapse, instability, and failure of the structure or structural members. The SLS is associated with states in which excessive deflection, vibration, and degradation make the structure or structural members unserviceable (EDCH 1996).

LSD is recommended by the Structural Plastics Design Manual. The service loads are factored to account for variations in applied loads, eccentricities, and differences between analytical and real behavior. Specific recommendations for load factors are not provided; however, example values are suggested for some cases. Capacity reduction factors are recommended for design of different structural members to account for long-term load effects and manufacturing variations. Example values are suggested. Design equations are based on the analysis of orthotropic plates, beams, and columns. In many cases equations for isotropic metallic structures are suggested where design equations are not available for FRP members. Material properties are obtained from manufacturers or from ASTM standard tests.

For the design of a pultruded column the following load and capacity reduction factors are given as an example (SPDM 1984, p. 717):

Load factors

All service loads = 2.5

Capacity reduction factors

Ultimate compressive strength = 0.5 Elastic moduli = 0.7

For the design of a pultruded beam the following load and capacity reduction factors are given as an example (SPDM 1984, p. 741):

Load factors

All service loads = 2.0

Capacity reduction factors

Ultimate compressive strength = 0.5

Ultimate tensile strength = 0.4

Ultimate shear strength = 0.3

Elastic moduli = 0.7

The load and capacity reduction factors suggested are based on standard industry practice and were not determined by probabilistic methods. They do not provide a measurable reliability index.

LSD is also recommended by Eurocomp Design Code and Handbook (EDCH). In the Eurocomp approach load factors are provided by the pertinent European Codes. Material partial safety factors, gm, are used to obtain appropriate capacity reduction factors. Material properties are divided by partial safety factors. According to the Eurocode the partial safety factors of FRP composites for structural applications account for (1) the method in which the material property data were obtained (gm>1), (2) the material manufacturing process (gm,2), and (3) the effects of environment and the duration of loading (gm,3). The material partial safety factor is given as the product of the three coefficients, gm = gm>1 x gm,2 x gm,3, and may not be less than 1.5 for ULSs and not less than 1.3 for SLSs. The following are examples of recommended values of the coefficients:

Material property data derived from theory |
gm,1 = |
= 1.5 |

Material property data derived from testing |
gm,1 = |
= 1.15 |

Fully cured pultruded material |
gm,2 = |

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