Existing Critical Flexural Capacity Prediction Models

For comparison purposes, two models from previous draft versions of the ASCE/ACMA Pre-Standard for Load and Resistance Factor Design (LRFD) of Pultruded Fiber Reinforced Polymer (FRP) Structures were applied and equated to the experimental data obtained for this study. The first model comes from the most recently publicly available draft of the ASCE/ACMA LRFD Pre-Standard proposed in November 2010. It should be noted that for direct comparison to the model proposed in Section 3.3, no resistance factors will be applied. For square and rectangular box members, two equations must be applied, and the minimum critical load value from these two equations is taken as the critical flexural load capacity. The first equation is used to calculate the nominal strength of member due to material rupture in tension or compression in the flanges or webs of members subjected to flexure, as calculated using Equation (3-15) { ( ) ( ) } (3-15) In which

FL,f = characteristic longitudinal strength of the flange (psi)

FL,w = characteristic longitudinal strength of the web (psi)

EL,f = characteristic value of the longitudinal modulus of the flange (psi)

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If = moment of inertia of the flanges about the axis of bending (in.4)

Iw = moment of inertia of the webs about the axis of bending (in.4)

yf = distance from the neutral axis to the extreme fiber of the flange (in.)

yw = distance from the neutral axis to the extreme fiber of the web (in.)

It is noted that when members have a longitudinal elastic modulus in the flange that is within 15 percent of the longitudinal elastic modulus of the web, the equation can be simplified as shown in Equation (3-16). For this study, it is assumed that the longitudinal elastic moduli in the flange and web are equal, therefore, the equation becomes

(3-16)

In which

FL = characteristic longitudinal strength of the member (psi)

I = moment of inertia of the member about the axis of bending (in.4₎

y = distance from the neutral axis to the extreme fiber of the member (in.)

The second equation required by this draft version is for the nominal strength of members due to local instability. All members that undergo compressive stresses due to flexure must be checked for local buckling of the flanges and webs. The local instability of the flange or web of a square or rectangular box section shall be determined by either Equation (3-17), for compression flange local buckling, or Equation (3-18), for web local buckling.

(3-17)

80 In which

fcr = critical buckling stress taken as the minimum of compression flange local buckling from Equation (3-20), and web local buckling from Equation (3-23)

EL,f = characteristic value of the longitudinal modulus of the flange (psi)

EL,w = characteristic value of the longitudinal modulus of the web (psi)

If = moment of inertia of the flanges about the axis of bending (in.4)

Iw = moment of inertia of the webs about the axis of bending (in.4)

It is noted that when members have a longitudinal elastic modulus in the flange that is within 15 percent of the longitudinal elastic modulus of the web, the Equations (3-17) and (3-18) can be simplified as shown in Equation (3-19). For this study, it is assumed that the longitudinal elastic moduli in the flange and web are equal, therefore, the equation becomes

_(3-19)

In which

fcr = critical buckling stress taken as the minimum of compression flange local buckling from Equation (3-20), and web local buckling from Equation (3-23)

I = moment of inertia of the member about the axis of bending (in.4)

y = distance from the neutral axis to the extreme fiber of the member (in.)

The critical buckling stress, fcr, due to compression flange local buckling is given by Equation (3-20) [ √( )( ) ( ) ( ₎ ] (3-20)

81 Where (3-21) { [( ) ( √ √ )]} (3-22)

The critical buckling stress, fcr, due to web local buckling is given by Equation (3-23)

( √ ) (3-23)

In which

EL,f = characteristic value of the longitudinal modulus of the flange (psi)

EL,w = characteristic value of the longitudinal modulus of the web (psi)

ET,f = characteristic value of the transverse modulus of the flange (psi)

ET,w = characteristic value of the transverse modulus of the web (psi)

GLT = characteristic value of the in-plane shear modulus (psi)

νLT = characteristic longitudinal Poisson’s ratio (in absence of available data νLT = 0.3)

bf = full width of the flange (in.)

h = full height of the member (in.) tf = thickness of the flange (in.)

tw = thickness of the web (in.)

ξ = coefficient of restraint

kr = rotational spring constant (lbf/rad)

The second model comes from a more recent draft of the ASCE/ACMA LRFD Pre- Standard proposed in May 2013. It should be noted that for direct comparison to the model

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proposed in Section 3.3, no resistance factors will be applied. In this newer draft, only one equation must be applied to determine the critical flexural load capacity of a square or rectangular box member. This single equation is based on the nominal strength of members due to local buckling, calculated as shown in Equation (3-24)

(3-24)

In which

St = transformed section modulus about the axis of bending (in.3), taking into account conditions of force equilibrium and strain compatibility

Fcr = critical buckling stress, taken as the lower value of local buckling stress of the compression flange from Equation (3-25) and local buckling stress of the web from Equation (3-26)

The local buckling stress of the compression flange, Fcrf, shall be calculated as shown in Equation (3-25), while the local buckling stress of the web, Fcrw, is defined as shown in Equation (3-26) ( _{) [√} ] ( ) (3-25) √ ( ) (3-26) In which

EL,f = characteristic value of the longitudinal modulus of the flange (psi)

EL,w = characteristic value of the longitudinal modulus of the web (psi)

ET,f = characteristic value of the transverse modulus of the flange (psi)

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GLT = characteristic value of the in-plane shear modulus (psi)

νLT = characteristic longitudinal Poisson’s ratio (in absence of available data νLT = 0.3)

bf = full width of the flange (in.)

tf = thickness of the flange (in.)

d = overall depth of section (in.) = h – tf

tw = thickness of the web (in.)

Results of the critical flexural capacity prediction models from the aforementioned drafts of the ASCE/ACMA LRFD Pre-Standard, compared with the experimental load capacities obtained for this study, can be found in Section 3.7.