Wood Diaphragm Deflections. I: Generalizing Standard Equations Using Mechanics-Based Derivations for Panel Construction

Data Availability Statement

Acknowledgments

Notation

A

area of diaphragm chord (in.²);

A_w

cross-sectional web area of diaphragm;

d

distance between axial tension and compression of diaphragm chords;

E

modulus of elasticity of diaphragm chords (lb_f/in.²);

$e_f$

fastener slip;

$e_{f\parallel }$

fastener slip along panel edge parallel to diaphragm load direction based on maximum diaphragm shear along diaphragm boundary;

e_f⊥

fastener slip along panel edge perpendicular to diaphragm load direction based on maximum diaphragm shear along diaphragm boundary;

e_n

nail slip measured parallel to nearest panel edge based on shear along diaphragm boundary (in.);

$e_n^{\mathrm{\prime }}$

change in panel framing diagonal length due to nail slip (in.);

$e_s^{\mathrm{\prime }}$

change in panel diagonal length due to shear strain (in.);

G

panel shear modulus (psi);

G_a

apparent diaphragm shear stiffness (kips/in.);

G_vt_v

panel in-plane, through-the-thickness, shear stiffness (lb_f/in. of depth) of WSP panels;

I

moment of inertia of diaphragm chords;

L

length of diaphragm span, perpendicular to diaphragm load direction (ft);

L′

length of cantilevered diaphragm span, perpendicular to diaphragm load direction (ft);

n_pl

number of panel lengths from edge of diaphragm to midspan of diaphragm;

$n_{\parallel }$

number of slip planes at panel-to-panel connections parallel to diaphragm load direction;

n_⊥

number of slip planes at panel-to-panel connections perpendicular to diaphragm load direction;

$P_{\parallel }$

panel dimension parallel to diaphragm load direction;

P_⊥

panel dimension perpendicular to diaphragm load direction;

$S_{\parallel }$

fastener spacing on panel edges parallel to diaphragm load direction;

S_⊥

fastener spacing on panel edges perpendicular to diaphragm load direction;

V(x)

total shear over width of diaphragm at location x;

V_n

shear force per nail;

V_s

total diaphragm shear at line of support;

$V_{\parallel }$

total shear on panel edge parallel to diaphragm load direction;

V_⊥

total shear on panel edge perpendicular to diaphragm load direction;

v

induced shear per unit length typically at diaphragm boundary/support line (lb/ft);

W

width of diaphragm, parallel to diaphragm load direction (ft);

W′

width of cantilevered diaphragm, parallel to diaphragm load direction (ft);

w

uniformly distributed applied diaphragm load;

x

distance from nearest diaphragm support to location of interest (ft);

x′

distance from free end of cantilever to location of interest (ft);

α

angle of shear strain component measured with respect to panel edges oriented parallel to applied diaphragm load direction, in geometric context;

β

angle of shear strain component measured with respect to panel edges oriented perpendicular to applied diaphragm load direction;

γ_xy

shear strain in panel or supporting framing;

Δ_c

diaphragm chord splice slip at induced unit shear (in.);

${\mathrm{\Delta }}_f^{\mathrm{\prime }}$

diaphragm slip deformation resulting from panel translation;

${\mathrm{\Delta }}_f^{\mathrm{″}}$

diaphragm slip deformation resulting from panel rotation;

${\mathrm{\Delta }}_p^{\mathrm{″}}$

panel slip deformation resulting from panel rotation;

δ_c

diaphragm deformation at midspan due to chord slip at single location;

δ_c,max

maximum diaphragm deformation due to chord slip at single location;

δ_chord

diaphragm deformation component from chord slip;

δ_dia

diaphragm deformation;

δ_flex

diaphragm deformation component from bending;

δ_shear

diaphragm deformation component from panel shear deformation;

δ_slip

diaphragm deformation component from panel fastener slip;

θ

angle of diaphragm rotation due to chord slip; and

τ_xy

shear stress per unit area in panel.

References