P L

where AZE is the axial stiffness of the member in compression.

For compression members serviceability (deflection) and ultimate (strength and stability) design states are considered. The calculated design stresses must be less than the critical strengths and critical buckling stresses according to the design basis selected.

16.1.4.2.1 Axial Shortening

For calculation of axial deformation the axial stiffness is taken as

where EL is the longitudinal modulus of the material. Note that it is often assumed that the tensile and compressive moduli of the FRP material are the same. If experimental tests indicate that the compressive modulus is not the same as the tensile modulus, then it should be used to determine axial shortening of columns. In the case of a nonhomogenous section the effective (composite) axial stiffness is used. To determine long-term axial shortening, the viscoelastic longitudinal modulus should be used.

16.1.4.2.2 Global Flexural Buckling

Global flexural (Euler) buckling of common pultruded columns has been studied in some detail (Barbero and Tomblin 1993; Zureick and Scott 1997; Zureick and Steffen 2000). It has been shown that the well-known Euler equation can be used. The classical equation, modified to account for shear deformation effects, is recommended (Zureick and Scott 1997; Zureick and Steffen 2000). The critical buckling stress including the effects of shear deformation is given as

where (kL/r)MAX is the maximum slenderness ratio for bending about the critical axis, k is the end restraint coefficient for the axis under consideration, L is the unbraced length of the column, and r is the radius of gyration for the axis under consideration. ktim is the Timoshenko shear coefficient and A is the cross-sectional area of the section. To neglect the effects of shear deformation, the term in the square brackets is set to unity. The Timoshenko shear coefficient used in this equation is the same as that used in the shear deformation beam theory.

16.1.4.2.3 Local Compressive Flange Buckling

The local buckling of unsupported flanges in columns is identical to the local buckling of compression flanges in beams and has been discussed in Section 16.1.4.1.3.

16.1.4.2.4 Local Compressive Web Buckling

Local buckling of column webs that are supported on both longitudinal edges is identical to that of the flanges supported on two longitudinal edges discussed previously. It is conservatively assumed that the web is simply supported at the longitudinal edges. The equation for determining this buckling stress is s 2P2tw ( ffiT VTeL gLT\ ,

Scr --¿rU(1 "VlVT) + 12(1 - VLVT) + ^"J (16 . 37)

and the length of the half-buckle wavelength is given by a — dw\ EL (16 . 38)

v eT

The equation for the case of the web fixed (built-in) at both edges is (for comparison purposes)

Scr dw \12(1 - VLVT) + 0 . 543 12(1 - VLVT) + 0 .543 6 J (16 .39)

and the length of the half-buckle wavelength is given by

4 El

16.1.4.2.5 Global Torsional Buckling

Open-section axially loaded compression members can buckle in a pure torsional mode. For doubly symmetric sections such as I and WF sections the critical torsional buckling stress (not including effects of shear deformation) is given as (Roberts 2002)

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