Page Comparison

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M_uc

821.813 kNm

AISC 358-16 (6.8-3)

F_t

750000 kN/m²

h_o

Mathinline

body	--uriencoded--$$ \normalsize h_o = d - \frac %7Bt_%7Bfo%7D%7D%7B2%7D + p_%7Bfo%7D = 450 - \frac %7B15%7D%7B2%7D + 72 = 514.5\; \mathrm%7Bmm%7D $$

h₁

Mathinline

body	--uriencoded--$$ \normalsize h_1 = d - 1.5 t_%7Bfo%7D - p_%7Bfi%7D = 450 - 1.5 \times 15 -72 = 355.5\; \mathrm%7Bmm%7D $$

d_b

Mathinline

body	--uriencoded--$$ \normalsize d_b \geq \sqrt%7B \dfrac %7B 2 M_%7Buc%7D%7D %7B\varphi \pi F_t(h_o + h_1)%7D %7D $$

Mathinline

body	--uriencoded--$$ \normalsize d_b \geq \sqrt%7B \dfrac %7B 2 \times 821.813%7D 813 \times 10%5e6%7D %7B0.90 \times \pi \times 750000 750 \times (514.5 + 355.5)%7D %7D =29.825 \; \; \mathrm%7Bmm%7D $$

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M_uc

821.813kNm

AISC 358-16 (6.8-5)

F_yp

275000 kN/m²

s

Mathinline

body	--uriencoded--$$ \normalsize s = \dfrac%7B1%7D%7B2%7D \sqrt%7B b_p g%7D = \dfrac%7B1%7D%7B2%7D \sqrt%7B 298 \times 154%7D = 107.112\; \mathrm%7Bmm%7D $$

Y_p

Mathinline

body	--uriencoded--$$ \small Y_p = \dfrac%7Bb_p%7D%7B2%7D \left [ h_1 \left ( \dfrac%7B1%7D%7Bp_%7Bfi%7D%7D + \dfrac%7B1%7D%7Bs%7D \right ) + h_0 \left ( \dfrac%7B1%7D%7Bp_%7Bfo%7D%7D + \dfrac%7B1%7D%7B2s%7D \right ) \right ] + \dfrac%7B2%7D%7Bg%7D \left [ h_1 \left ( p_%7Bfi%7D +s \right ) + h_o \left ( d_%7Be%7D + p_%7Bfo%7D \right ) \right ] $$

Y_p

Mathinline

body	--uriencoded--$$ \normalsize Y_p = \dfrac%7B298%7D%7B2%7D \left [ 355.5 \left ( \dfrac%7B1%7D%7B72%7D + \dfrac%7B1%7D%7B107.112%7D \right ) + 514.5 \left ( \dfrac%7B1%7D%7B72%7D + \dfrac%7B1%7D%7B2 \times 107.112 %7D \right ) \right ] $$

Mathinline

body	--uriencoded--$$ \normalsize + \dfrac%7B2%7D%7B154%7D \left [ 355.5 \left ( 72 + 107.112 \right ) + 514.5 \left ( 72 + 72 \right ) \right ] =4441.914 \; \mathrm%7Bmm%7D $$

t_p

Mathinline

body	--uriencoded--$$ \normalsize t_p \geq \sqrt%7B \dfrac %7B 1.11 M_%7Buc%7D%7D %7B\varphi F_%7Byc%7DY_p%7D %7D = \sqrt%7B \dfrac %7B 1.11 \times 821.813%7D 813\times 10%5e%7B6%7D%7D %7B 1 \times 275 \times 10%5e%7B-3%7D \times 4441.914%7D %7D = 27.327 \; \mathrm%7Bmm%7D $$

Required	Available	Ratio	Control
27.327 mm	30 mm	0.911	√

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t_bw

9 mm

AISC 358-16 (6.8-9)

F_yb

275000 kN/m²

F_ys

275000 kN/m²

t_s

12 mm

Mathinline

body	--uriencoded--$$ \normalsize t_s \geq t_%7Bbw%7D \dfrac %7B F_%7Byb%7D%7D %7BF_%7Bys%7D%7D $$

Mathinline

body	--uriencoded--$$ \normalsize 12 \; \mathrm%7Bmm%7D \geq 9 \times \dfrac %7B 275000%7D %7B275000%7D =9 \; \mathrm%7Bmm%7D $$

Required	Available	Ratio	Control
9 mm	12 mm	0.750	√

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A_b

Mathinline

body	--uriencoded--$$ \normalsize A_%7Bb%7D = \dfrac %7B \pi d%5e2%7D%7B4%7D = \dfrac %7B \pi 36%5e2%7D%7B4%7D =1017.876 \; \mathrm%7Bmm%5e2%7D $$

AISC 358-16 6.8.11

F_n

Mathinline

body	--uriencoded--$$ \normalsize F_n = 0.450F_%7Bub%7D = 0.450 \times 1000 = 450 \; \mathrm%7BN/mm%5e2%7D $$

R_n

Mathinline

body	--uriencoded--$$ \normalsize R_n = F_%7Bn%7DA_b = 4 \times 450 \times 1017.876 \times 10%5e%7B-3%7D = 1832.177 \; \; \mathrm%7BkN%7D $$

ΦR_n

Mathinline

body	--uriencoded--$$ \normalsize \varphi R_n = 0.9 \times 1832.177 = 1648.959 \; \; \mathrm%7BkN%7D $$

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d_h

36+3=39 mm

L_c,edge

Mathinline

body	--uriencoded--$$ \normalsize L_%7Bc,edge%7D = L_e - 0.5d_h = 72 - 0.5 \times 39 = 52.5 $$\; \mathrm%7Bmm%7D$$

R_n

Mathinline

body	--uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2L_c \times t \times F_u \\2.4d \times t \times F_u \end%7Bmatrix%7D\right] \end%7Baligned%7D

AISC 358-16 6.8-12

R_n-edge

Mathinline

body	--uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2(52.5)(30)(410000 \times 10%5e%7B-3%7D) \\2.4(36)(30)(410000 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D =774.9 \; \; \mathrm%7BkN%7D

L_c,spacing

Mathinline

body	--uriencoded--$$ \normalsize L_%7Bc,spacing%7D = 72 + 72 + 15 - 39 = 120 \; \mathrm%7Bmm%7D $$

R_n-spacing

Mathinline

body	--uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2(120)(30)(410000 \times 10%5e%7B-3%7D) \\2.4(36)(30)(410000 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D =1062.72\; \mathrm%7BkN%7D

R_n

Mathinline

body	--uriencoded--$$ \normalsize R_n = n_e R_%7Bn-edge%7D + n_s R_%7Bn-spacing%7D $$

Mathinline

body	--uriencoded--$$ \normalsize R_n = 2 \times 774.9 + 2 \times 1062.72 = 3675.24 \; \; \mathrm%7BkN%7D $$

ΦR_n

Mathinline

body	--uriencoded--$$ \normalsize \varphi R_n = 0.9 \times 3675.24 = 3307.716 \; \; \mathrm%7BkN%7D $$

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d_b

36 mm

R_n

Mathinline

body	--uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2L_c \times t \times F_u \\2.4d \times t \times F_u \end%7Bmatrix%7D\right] \end%7Baligned%7D

AISC 358-16 6.8-12

R_n-edge

Mathinline

body	--uriencoded--$$ \normalsize R_n = [ 2.4 (36) (31) (410000 \times 10%5e%7B-3%7D ) ] = 1098.144\; \mathrm%7BkN%7D $$

L_c,spacing

Mathinline

body	--uriencoded--$$ \normalsize L_%7Bc,spacing%7D = 72+ 72 +15 - 39 = 120 $$\; \mathrm%7Bmm%7D$$

R_n-spacing

Mathinline

body	--uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2(120)(31)(410000 \times 10%5e%7B-3%7D) \\2.4(36)(31)(410000 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D = 1098.144\; \mathrm%7BkN%7D

R_n

Mathinline

body	--uriencoded--$$ \normalsize R_n = n_e R_%7Bn-edge%7D + n_s R_%7Bn-spacing%7D $$

Mathinline

body	--uriencoded--$$ \normalsize R_n = 2 \times 1098.144 + 2 \times 1098.144 = 4392.576 \; \; \mathrm%7BkN%7D $$

ΦR_n

Mathinline

body	--uriencoded--$$ \normalsize \varphi R_n = 0.9 \times 4392.576 = 3953.318 \; \; \mathrm%7BkN%7D $$

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F_yp

275000 kN/m²

AISC 358-16

(6.7.6) 3

t_bw

9 mm

F _e

490000 kN/m²

w

Mathinline

body	--uriencoded--$$ \normalsize w \geq \dfrac %7B \varphi_t F_%7Byb%7D t_%7Bbw%7D%7D %7B2 \times \varphi \times 0.6 F_e \times 1.5 \times 0.707%7D%7D $$

Mathinline

body	--uriencoded--$$ \normalsize = \dfrac %7B 0.9 \times 275 \times 10%5e%7B-3%7D \times 9%7D %7B2 \times 0.75 \times 0.6 \times 490 \times 10%5e%7B-3%7D \times 1.5 \times 0.707%7D%7D = 4.763 \; \; \mathrm%7Bmm%7D $$

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M_uc

821.813 kNm

AISC 358-16 (6.8-13)

F_yp

275000 kN275 N/mmm²

s

Mathinline

body	--uriencoded--$$ \normalsize s = \dfrac%7B1%7D%7B2%7D \sqrt%7B b_f g%7D = \dfrac%7B1%7D%7B2%7D \sqrt%7B 300 \times 154%7D = 107.471\; \mathrm%7Bmm%7D $$

c

Mathinline

body	--uriencoded--$$ \normalsize c = p_%7Bfo%7D + t_%7Bfo%7D + p_%7Bfi%7D = 72 + 16 + 72 = 160\; \mathrm%7Bmm%7D $$

Y_c

Mathinline

body	--uriencoded--$$ \small Y_c = \dfrac%7Bb_f%7D%7B2%7D \left [ h_1 \left ( \dfrac%7B1%7D%7Bs%7D \right ) + h_0 \left ( \dfrac%7B1%7D%7Bs%7D \right ) \right ] + \dfrac%7B2%7D%7Bg%7D \left [ h_1 \left ( s + \dfrac%7B3c%7D%7B4%7D \right ) + h_0 \left ( s + \dfrac%7Bc%7D%7B4%7D \right ) + \dfrac%7Bc%5e2%7D%7B2%7D \right ] + \dfrac%7Bg%7D%7B2%7D $$

Y_c

Mathinline

body	--uriencoded--$$ \normalsize Y_c = \dfrac%7B300%7D%7B2%7D \left [ 355.5 \left ( \dfrac%7B1%7D%7B107.471%7D \right ) + 514.5 \left ( \dfrac%7B1%7D%7B107.471%7D \right ) \right ] $$

Mathinline

body	--uriencoded--$$ \normalsize + \dfrac%7B2%7D%7B154%7D \left [ 355.5 \left ( 107.471 + \dfrac%7B3 \times 160 %7D%7B4%7D \right ) + 514.5 \left ( 107.471 + \dfrac%7B160%7D%7B4%7D \right ) $$

Mathinline

body	--uriencoded--$$ \normalsize + \dfrac%7B160%5e2%7D%7B2%7D \right ] + \dfrac%7B154%7D%7B2%7D =5054.57 \; \mathrm%7Bmm%7D $$

t_cf

Mathinline

body	--uriencoded--$$ \normalsize t_%7Bcf%7D \geq \sqrt%7B \dfrac %7B 1.11 M_%7Buc%7D%7D %7B\varphi F_%7Byc%7DY_c%7D %7D = \sqrt%7B \dfrac %7B 1.11 \times 821.813%7D 813 \times 10%5e%7B6%7D %7D %7B 1 \times 275 \times 10%5e%7B-3%7D \times 5054.57%7D %7D = 25.618\; \mathrm%7Bmm%7D $$

Required	Available	Ratio	Control
25.618 mm	31 mm	0.826	√

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