I = \frac{b h^{3}}{12},\quad Z = \frac{b h^{2}}{6}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>I</mi><mo>=</mo>
    <mfrac><mrow><mi>b</mi><msup><mi>h</mi><mn>3</mn></msup></mrow><mn>12</mn></mfrac>
    <mo>,</mo>
    <mi>Z</mi><mo>=</mo>
    <mfrac><mrow><mi>b</mi><msup><mi>h</mi><mn>2</mn></msup></mrow><mn>6</mn></mfrac>
  </mrow>
</math>

I = (b h^3) / 12,  Z = (b h^2) / 6

{b*h^3/12, b*h^2/6}

Iz := b*h^3/12;  Z := b*h^2/6;

I = b*h^3/12;  Z = b*h^2/6;  % b는 깊이(mm), h는 두께(mm)

I = b h^3/12,  Z = b h^2/6

\delta = \frac{5 w L^{4}}{384 E I}\ \text{(simply supported)},\quad \delta = \frac{w L^{4}}{384 E I}\ \text{(fixed ends)}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>δ</mi><mo>=</mo>
    <mfrac><mrow><mn>5</mn><mi>w</mi><msup><mi>L</mi><mn>4</mn></msup></mrow><mrow><mn>384</mn><mi>E</mi><mi>I</mi></mrow></mfrac>
    <mo>,</mo>
    <mi>δ</mi><mo>=</mo>
    <mfrac><mrow><mi>w</mi><msup><mi>L</mi><mn>4</mn></msup></mrow><mrow><mn>384</mn><mi>E</mi><mi>I</mi></mrow></mfrac>
  </mrow>
</math>

delta = (5 w L^4) / (384 E I),  delta = (w L^4) / (384 E I)

{5*w*L^4/(384*Ey*Iz), w*L^4/(384*Ey*Iz)}

delta_simple := 5*w*L^4/(384*E*Iz);  delta_fixed := w*L^4/(384*E*Iz);

delta_simple = 5*w*L^4/(384*E*I);  delta_fixed = w*L^4/(384*E*I);  % w는 N/mm, L은 mm, E는 N/mm^2, I는 mm^4

δ = 5 w L^4/(384 E I),  δ = w L^4/(384 E I)

\delta = \frac{P L^{3}}{48 E I}\ \text{(simply supported)},\quad \delta = \frac{P L^{3}}{192 E I}\ \text{(fixed ends)}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>δ</mi><mo>=</mo>
    <mfrac><mrow><mi>P</mi><msup><mi>L</mi><mn>3</mn></msup></mrow><mrow><mn>48</mn><mi>E</mi><mi>I</mi></mrow></mfrac>
    <mo>,</mo>
    <mi>δ</mi><mo>=</mo>
    <mfrac><mrow><mi>P</mi><msup><mi>L</mi><mn>3</mn></msup></mrow><mrow><mn>192</mn><mi>E</mi><mi>I</mi></mrow></mfrac>
  </mrow>
</math>

delta = (P L^3) / (48 E I),  delta = (P L^3) / (192 E I)

{P*L^3/(48*Ey*Iz), P*L^3/(192*Ey*Iz)}

delta_simple := P*L^3/(48*E*Iz);  delta_fixed := P*L^3/(192*E*Iz);

delta_simple = P*L^3/(48*E*I);  delta_fixed = P*L^3/(192*E*I);  % P는 N, L은 mm, E는 N/mm^2, I는 mm^4

δ = P L^3/(48 E I),  δ = P L^3/(192 E I)

\delta_{\mathrm{long}} = k_c \, \delta_0,\quad n = \frac{L}{\delta_{\mathrm{long}}}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <msub><mi>δ</mi><mi>long</mi></msub><mo>=</mo><msub><mi>k</mi><mi>c</mi></msub><msub><mi>δ</mi><mn>0</mn></msub>
    <mo>,</mo>
    <mi>n</mi><mo>=</mo><mfrac><mi>L</mi><msub><mi>δ</mi><mi>long</mi></msub></mfrac>
  </mrow>
</math>

delta_(long) = k_c * delta_0,  n = L / delta_(long)

{kc*delta0, L/(kc*delta0)}

delta_long := kc*delta0;  n := L/delta_long;

delta_long = kc*delta0;  n = L/delta_long;  % kc는 크리프 계수, delta0은 올린 직후의 처짐(mm)

δ_long = k_c δ_0,  n = L/δ_long

L_{\max} = \sqrt[4]{\frac{384 E I \delta_a}{5 w k_c}},\quad w_{\max} = \frac{384 E I \delta_a}{5 k_c L^{4}}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <msub><mi>L</mi><mi>max</mi></msub><mo>=</mo>
    <mroot><mfrac><mrow><mn>384</mn><mi>E</mi><mi>I</mi><msub><mi>δ</mi><mi>a</mi></msub></mrow><mrow><mn>5</mn><mi>w</mi><msub><mi>k</mi><mi>c</mi></msub></mrow></mfrac><mn>4</mn></mroot>
    <mo>,</mo>
    <msub><mi>w</mi><mi>max</mi></msub><mo>=</mo>
    <mfrac><mrow><mn>384</mn><mi>E</mi><mi>I</mi><msub><mi>δ</mi><mi>a</mi></msub></mrow><mrow><mn>5</mn><msub><mi>k</mi><mi>c</mi></msub><msup><mi>L</mi><mn>4</mn></msup></mrow></mfrac>
  </mrow>
</math>

L_max = root(4)((384 E I delta_a) / (5 w k_c)),  w_max = (384 E I delta_a) / (5 k_c L^4)

{(384*Ey*Iz*deltaA/(5*w*kc))^(1/4), 384*Ey*Iz*deltaA/(5*kc*L^4)}

Lmax := (384*E*Iz*deltaA/(5*w*kc))^(1/4);  wmax := 384*E*Iz*deltaA/(5*kc*L^4);

Lmax = (384*E*I*deltaA/(5*w*kc))^(1/4);  wmax = 384*E*I*deltaA/(5*kc*L^4);  % deltaA는 허용 처짐(mm), kc는 크리프 계수

L_max = (384 E I δ_a/(5 w k_c))^(1/4),  w_max = 384 E I δ_a/(5 k_c L^4)

M = \frac{w L^{2}}{8},\quad \sigma = \frac{M}{Z}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>M</mi><mo>=</mo>
    <mfrac><mrow><mi>w</mi><msup><mi>L</mi><mn>2</mn></msup></mrow><mn>8</mn></mfrac>
    <mo>,</mo>
    <mi>σ</mi><mo>=</mo><mfrac><mi>M</mi><mi>Z</mi></mfrac>
  </mrow>
</math>

M = (w L^2) / 8,  sigma = M / Z

{w*L^2/8, (w*L^2/8)/Z}

M := w*L^2/8;  sigma := M/Z;

M = w*L^2/8;  sigma = M/Z;  % w는 N/mm, L은 mm, Z는 mm^3

M = w L^2/8,  σ = M/Z