213B FINAL EQUATIONS

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Last updated 4:58 AM on 5/13/26
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11 Terms

1
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Moment - Bending

M = Moment (ft lbs)

W = Load per unit length (lbs per ft)

L = Length of member (ft)

8 = Constant

<p>M = Moment (ft lbs)</p><p>W = Load per unit length (lbs per ft)</p><p>L = Length of member (ft)</p><p>8 = Constant</p>
2
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Max Bending Stress - Bending

fb = Max Bending Stress (lbs per in2)

M = Moment (lbs ft) [convert to lbs in by multiplying by 12]

S = Section Modulus (in3)

<p>f<sub>b</sub> = Max Bending Stress (lbs per in<sup>2</sup>)</p><p>M = Moment (lbs ft) <em>[convert to lbs in by multiplying by 12]</em></p><p>S = Section Modulus (in<sup>3</sup>)</p>
3
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Section Modulus - Bending

S = Section Modulus (in3)

b = Width (in) [shorter dimension of section]

d = Depth (in) [longer dimension of section]

6 = Constant [Six→Section]

<p>S = Section Modulus (in<sup>3</sup>)</p><p>b = Width (in) <em>[shorter dimension of section]</em></p><p>d = Depth (in) <em>[longer dimension of section]</em></p><p>6 = Constant <em>[</em><strong><em><u>S</u></em></strong><em>ix→</em><strong><em><u>S</u></em></strong><em>ection]</em></p>
4
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Shear Force - Shear

V = Shear Force (lbs)

W = Load per unit length (lbs per ft)

L = Length of member (ft)

½ = Constant

<p>V = Shear Force (lbs)</p><p>W = Load per unit length (lbs per ft)</p><p>L = Length of member (ft)</p><p>½ = Constant</p>
5
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Max Shear Stress (Rectangular) - Shear

fv = Max Shear Stress (lbs per in2)

V = Shear (lbs)

A = Cross Sectional Area (in2)

3/2 = Constant

<p>f<sub>v</sub> = Max Shear Stress (lbs per in<sup>2</sup>)</p><p>V = Shear (lbs)</p><p>A = Cross Sectional Area (in<sup>2</sup>)</p><p>3/2 = Constant</p>
6
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Max Shear Stress (Average Uniformly Distributed) - Shear

fv = Max Shear Stress (lbs per in2)

V = Shear (lbs)

A = Cross Sectional Area (in2)

<p>f<sub>v</sub> = Max Shear Stress (lbs per in<sup>2</sup>)</p><p>V = Shear (lbs)</p><p>A = Cross Sectional Area (in<sup>2</sup>)</p>
7
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Inertia - Deflection

I = Inertia (in4)

b = Width (in) [Shorter dimension of cross-section]

d = Depth (in) [Longer dimension of cross-section]

12 = Constant

<p>I = Inertia (in<sup>4</sup>)</p><p>b = Width (in) [Shorter dimension of cross-section]</p><p>d = Depth (in) [Longer dimension of cross-section]</p><p>12 = Constant</p>
8
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Deflection - Deflection

W = Load per unit length (lbs per ft)

L = Member length (ft)

E = Elastic Modulus (lbs per ft2) [given]

I = Inertia (in4)

5 = Constant

384 = Constant

<p>W = Load per unit length (lbs per ft)</p><p>L = Member length (ft)</p><p>E = Elastic Modulus (lbs per ft<sup>2</sup>) <em>[given]</em></p><p>I = Inertia (in<sup>4</sup>)</p><p>5 = Constant</p><p>384 = Constant</p>
9
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Max Crushing Stress - Crushing

Fc = Max Crushing Stress (lbs per in2)

F = Load Force (lbs)

A = Cross Sectional Area (in2)

<p>Fc = Max Crushing Stress (lbs per in<sup>2</sup>)</p><p>F = Load Force (lbs)</p><p>A = Cross Sectional Area (in<sup>2</sup>)</p>
10
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Load Force - Crushing

F = Load Force (lbs)

WL = Live Load (lbs per ft2)

WD = Dead Load (lbs per ft2)

AT = Tributary Area (ft2)

<p>F = Load Force (lbs)</p><p>W<sub>L</sub> = Live Load (lbs per ft<sup>2</sup>)</p><p>W<sub>D</sub> = Dead Load (lbs per ft<sup>2</sup>)</p><p>A<sub>T</sub> = Tributary Area (ft<sup>2</sup>)</p>
11
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Critical Buckling Load - Buckling

Fcr = Critical Buckling Load (lbs)

E = Elastic Modulus (lbs per in2)

I = Inertia (in4)

L = Length of Column (ft)

pi = 3.14

<p>F<sub>cr</sub> = Critical Buckling Load (lbs)</p><p>E = Elastic Modulus (lbs per in<sup>2</sup>)</p><p>I = Inertia (in<sup>4</sup>)</p><p>L = Length of Column (ft)</p><p>pi = 3.14</p>