Bending

 

Stress vs Grain Direction

longitudinal stresses (parallel-to-grain) are typical

cross-grain tension should be avoided  (from a tension force, bending moment, etc)

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reference bending design values are only for longitudinal bending stresses

 

Span Length

1. clear span

2. center-of-support to center-of-support = nominal span length used in textbook

3. clear span + require bearing length (half at each end) = definition in NDS section 3.2.1

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Bending Stress

ASD:  f_b = Mc/I = M/S ≤ F'_b  (CE 110 chapter 8)
LRFD:  M_u ≤ M'_n = F'_bnS

 

Industry Vocabulary

bending moment around strong (x) axis

• loaded edgewise
• edgewise bending
• load applied to narrow face
• load applied ⊥ to wide face of lams

f_bx and F'_bx

bending moment around weak (y) axis

• loaded flatwise
• flatwise bending
• load applied to wide face
• load applied // to wide face of lams

f_by and F'_by

 

 Mechanics Assumptions

• solid, homogeneous, isotropic material
• plane sections remain plane before/after loading
• linear, elastic relationship between stress and strain

F'_b = F_b(C_D)(C_M)(C_t)(C_L)(C_F or C_V)(C_fu)(C_c)(C_i)(C_r)
F'_bn = F_bn(Φ_b)(λ)(C_M)(C_t)(C_L)(C_F or C_V)(C_fu)(C_c)(C_i)(C_r)

 

Reference Bending Design Values

F_b = F_bx = F_by for visually graded sawn lumber, except for beams & stringers and decking  (use C_fu for F_by)

F_b = F_bx for beams & stringers  (use C_F to get F_by)  (see textbook Example 6.4 and NDS section 4.1.7 for discussion on middle vs outer thirds of B&S lumber)
F_b = F_by for decking  (already incorporates C_fu)

F_bx and F_by are provided for glulams

F⁺_bx and F^-_bx are needed when positive and negative moments exist on the same side of beam (or if beam is installed upside down)

 

Notches

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stress concentrations

NDS section 4.4.3

• < 1/6 depth
• not in middle third of span
• etc

NDS section 5.4.4 for glulams