Page Comparison

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M_uc

861.35 kNm

AISC 358-16 (6.8-4)

F_t

750000 kN/m²

h₁

Mathinline

body	--uriencoded--$$ \normalsize h_%7B1%7D = d - \dfrac%7Bt_%7Bfo%7D%7D %7B2%7D + p_%7Bfo%7D + p_b = 450 - \dfrac %7B15%7D %7B2%7D + 50 + 90 = 582.5 \; \mathrm%7Bmm%7D $$

h₂

Mathinline

body	--uriencoded--$$ \normalsize h_%7B2%7D = d - \dfrac%7Bt_%7Bfo%7D%7D %7B2%7D + p_%7Bfo%7D = 450 - \dfrac %7B15%7D %7B2%7D + 50 = 492.5 $$\; \mathrm%7Bmm%7D$$

h₃

Mathinline

body	--uriencoded--$$ \normalsize h_%7B3%7D = d - t_%7Bfo%7D - p_%7Bfi%7D - \dfrac%7B t_%7Bfo%7D%7D%7B2%7D = 450 - 15- 50 - \dfrac%7B 15%7D%7B2%7D = 377.5\; \mathrm%7Bmm%7D $$

h₄

Mathinline

body	--uriencoded--$$ \normalsize h_%7B4%7D = d - t_%7Bfo%7D - p_%7Bfi%7D - \dfrac%7B t_%7Bfo%7D%7D%7B2%7D - p_b = 450 - 15- 50 - \dfrac%7B 15%7D%7B2%7D - 90 $$

Mathinline

body	--uriencoded--$$ \normalsize h_%7B4%7D = 287.5\; \mathrm%7Bmm%7D $$

d_b

Mathinline

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

Mathinline

body	--uriencoded--$$ \small = \sqrt%7B \dfrac %7B 2 \times 861.35 \times10%5e6 %7D %7B 0.90 \times \pi \times 750000 750 \times (582.5 + 492.5 + 377.5 +287.5 )%7D %7D = 21.607 \; \; \mathrm%7Bmm%7D $$

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M_uc

861.35 kNm

AISC 358-16 (6.8-5)

F_yp

275000 kN275 N/mmm²

s

Mathinline

body	--uriencoded--$$ \normalsize s = \dfrac%7B1%7D%7B2%7D \sqrt%7B b_pg%7D = \dfrac%7B1%7D%7B2%7D \sqrt%7B 280 \times 140%7D = 98.995\; \mathrm%7Bmm%7D $$

Y_p

Mathinline

body	--uriencoded--$$ \normalsize Y_p = \dfrac%7Bb_p%7D%7B2%7D \left [ h_1\dfrac%7B1%7D%7B2d_e%7D + h_2 \dfrac%7B1%7D%7Bp_%7Bfo%7D%7D + h_3 \dfrac%7B1%7D%7Bp_%7Bfi%7D%7D + h_4 \dfrac%7B1%7D%7Bs%7D \right ] + \dfrac%7B2%7D%7Bg%7D \left [ h_1 \left (d_e + \dfrac%7Bp_b%7D%7B4%7D \right ) $$

Mathinline

body	--uriencoded--$$ \normalsize + h_2 \left (p_%7Bfo%7D + \dfrac%7B3p_b%7D%7B4%7D \right ) + h_3 \left (p_%7Bfi%7D + \dfrac%7Bp_b%7D%7B4%7D \right ) + h_4 \left (s + \dfrac%7B3p_b%7D%7B4%7D \right ) + p_b%5e2 \right ] + g $$

Y_p

Mathinline

body	--uriencoded--$$ \normalsize Y_p = \dfrac%7B280%7D%7B2%7D \left [ 582.5\dfrac%7B1%7D%7B2 \times 70%7D + 492.5 \dfrac%7B1%7D%7B50%7D + 377.5 \dfrac%7B1%7D%7B50%7D + 287.5 \dfrac%7B1%7D%7B98.995%7D \right ] $$

Mathinline

body	--uriencoded--$$ \normalsize + \dfrac%7B2%7D%7B140%7D \left [ 582.5 \left (70 + \dfrac%7B90%7D%7B4%7D \right ) + 492.5 \left (50 + \dfrac%7B3 \times 90 %7D%7B4%7D \right ) +377.5 \left (50 + \dfrac%7B90%7D%7B4%7D \right ) $$

Mathinline

body	--uriencoded--$$ \normalsize + 287.5 \left (98.995 + \dfrac%7B3 \times 90%7D%7B4%7D \right ) + 90%5e2 \right ] + 140 =6352.03\; \mathrm%7Bmm%7D $$

t_p

Mathinline

body	--uriencoded--$$ \normalsize t_p \geq \sqrt%7B \dfrac %7B 1.11 M_%7Buc%7D%7D %7B\varphi F_%7Byc%7DY_p%7D %7D = \sqrt%7B \dfrac %7B 1.11 \times 861.35%7D 35\times 10%5e%7B6%7D %7D %7B 1 \times 275 \times 10%5e%7B-3%7D \times 6352.03%7D %7D = 23.395 \; \mathrm%7Bmm%7D $$

Required	Available	Ratio	Control
23.395 mm	30 mm	0.780	√

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t_bw

9 mm

AISC 358-16 (6.8-9)

F_yb

275000 kN275 N/mmm²

F_ys

275000 kN275 N/mmm²

t_s

15 mm

Mathinline

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

Mathinline

body	--uriencoded--$$ \normalsize 15 \geq 9 \times \dfrac %7B 275000%7D 275%7D %7B275%7D = 9 \; \mathrm%7Bmm%7D $$

Required	Available	Ratio	Control
9 mm	15 mm	0.600	√

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F_ys

275000 kN/m²

AISC DG 4-2^nd

3.2.10

t_s

15 mm

F_e

490000 kN/m²

w

Mathinline

body	--uriencoded--$$ \normalsize w \geq \dfrac %7B \varphi_v 0.6 F_%7Bys%7D t_%7Bs%7D%7D %7B2 \varphi 0.6 F_e 0.707%7D%7D $$

Mathinline

body	--uriencoded--$$ \normalsize = \dfrac %7B 1 \times 0.6 \times 275 \times 10%5e%7B-3%7D \times 15%7D %7B2 \times 0.75 \times 0.6 \times 490 \times 10%5e%7B-3%7D \times 0.707%7D%7D = 7.938 \; \; \mathrm%7Bmm%7D $$

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F_ys

275000 kN/m²

AISC DG 4-2^nd

3.2.10

t_s

15 mm

F_e

490000 kN/m²

w

Mathinline

body	--uriencoded--$$ \normalsize w \geq \dfrac %7B \varphi_t F_%7Bys%7D t_%7Bs%7D%7D %7B2 \times \varphi \times 0.6 F_e \times1.5 \times 0.707%7D%7D $$

Mathinline

body	--uriencoded--$$ \normalsize = \dfrac %7B 0.9 \times 275 \times 10%5e%7B-3%7D \times 15%7D %7B2 \times 0.75 \times 0.6 \times 490 \times 10%5e%7B-3%7D \times 1.5 \times 0.707%7D%7D = 7.938 \; \; \mathrm%7Bmm%7D $$

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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--$$ \normalsize R_n = F_%7Bn%7DA_b = 8 \times 450 \times 706.858 \times 10%5e%7B-3%7D = 2544.6888 \; \; \mathrm%7BkN%7D $$

ΦR_n

Mathinline

body	--uriencoded--$$ \normalsize \varphi R_n = 0.90 \times 2544.6888 = 2290.22 \; \; \mathrm%7BkN%7D $$

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d_h

30+3=33 mm

L_c,edge

Mathinline

body	--uriencoded--$$ \normalsize L_%7Bc,edge%7D = L_e - 0.5d_h = 70 - 0.5 \times 33 = 53.5 $$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(53.5)(30)(410000 410 \times 10%5e%7B-3%7D) \\2.4(30)(30)(410000 410 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D =789.66\; \mathrm%7BkN%7D

L_c,spacing1

Mathinline

body	--uriencoded--$$ \normalsize L_%7Bc,spacing1%7D = 50 + 50 + 15 - 33 = 82 $$

R_n-spacing1

Mathinline

body	--uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2(82)(30)(410000 410 \times 10%5e%7B-3%7D) \\2.4(30)(30)(410000 410 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D =885.6 \; \; \mathrm%7BkN%7D

L_c,spacing2

Mathinline

body	--uriencoded--$$ \normalsize L_%7Bc,spacing2%7D = 90 - 33 = 57 $$

R_n-spacing2

Mathinline

body	--uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2(57)(30)(410000 410 \times 10%5e%7B-3%7D) \\2.4(30)(30)(410000 410 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D =841.32 \; \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--$$ \normalsize = 2 \times 789.66 + 2 \times 885.6 + 4 \times 841.32 = 6715.8 \; \; \mathrm%7BkN%7D $$

ΦR_n

Mathinline

body	--uriencoded--$$ \normalsize \varphi R_n = 0.90 \times 6715.8 = 6044.22 \; \; \mathrm%7BkN%7D $$

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d_h

30+3=33 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--$$ \normalsize R_n = \left [ 2.4 (30) (31) (410000 410 \times 10%5e%7B-3%7D ) \right ] =915.12\; \mathrm%7BkN%7D $$

L_c,spacing1

Mathinline

body	--uriencoded--$$ \normalsize L_%7Bc,spacing1%7D = 50 + 50 + 15 - 33 = 82 $$

R_n-spacing1

Mathinline

body	--uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2(82)(31)(410000 410 \times 10%5e%7B-3%7D) \\2.4(30)(31)(410000 410 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D =915.12\; \mathrm%7BkN%7D

L_c,spacing2

Mathinline

body	--uriencoded--$$ \normalsize L_%7Bc,spacing2%7D = 90 - 33 = 57 $$

R_n-spacing2

Mathinline

body	--uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2(57)(31)(410000 410 \times 10%5e%7B-3%7D) \\2.4(30)(31)(410000 410 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D =869.364\; \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--$$ \normalsize = 2 \times 789.66 + 2 \times 885.6 + 4 \times 841.32 = 6715.8 \; \; \mathrm%7BkN%7D $$

ΦR_n

Mathinline

body	--uriencoded--$$ \normalsize \varphi R_n = 0.90 \times 7137.936 = 6424.142 \; \; \mathrm%7BkN%7D $$

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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--$$ \normalsize w \geq \dfrac %7B \varphi_t F_%7Byb%7D t_%7Bbw%7D%7D %7B2 \times \varphi \times 0.6 F_e \times1.5 \times 0.707%7D%7D $$

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

861.352 kNm

AISC 358-16 (6.8-13)

F_yp

275000 kN/m²

s

Mathinline

body	--uriencoded--$$ \normalsize s = \dfrac%7B1%7D%7B2%7D \sqrt%7B b_f g%7D = \dfrac%7B1%7D%7B2%7D \sqrt%7B 300 \times 140%7D = 102.469 $$

c

Mathinline

body	--uriencoded--$$ \normalsize c = p_%7Bfo%7D + t_%7Bfo%7D + p_%7Bfi%7D = 50 + 16 + 50 = 116 $$

Y_c

Mathinline

body	--uriencoded--$$ \normalsize Y_c = \dfrac%7Bb_f%7D%7B2%7D \left [ h_1 \left ( \dfrac%7B1%7D%7Bs%7D \right ) + h_4 \left ( \dfrac%7B1%7D%7Bs%7D \right ) \right ] $$

Mathinline

body	--uriencoded--$$ \normalsize + \dfrac%7B2%7D%7Bg%7D \left [ h_1 \left ( p_b + s + \dfrac%7Bc%7D%7B4%7D \right ) + h_2 \left ( \dfrac%7Bp_b%7D%7B2%7D + \dfrac%7Bc%7D%7B4%7D \right ) + h_3 \left ( \dfrac%7Bp_b%7D%7B2%7D + \dfrac%7Bc%7D%7B2%7D \right ) +h_4(s) \right ] + \dfrac%7Bg%7D%7B2%7D $$

Y_c

Mathinline

body	--uriencoded--$$ \normalsize Y_c = \dfrac%7B300%7D%7B2%7D \left [ 582/5 \left ( \dfrac%7B1%7D%7B102.469%7D \right ) + 287.5 \left ( \dfrac%7B1%7D%7B102.469%7D \right ) \right ] $$

Mathinline

body	--uriencoded--$$ \normalsize + \dfrac%7B2%7D%7B140%7D \left [ 582.5 \left ( 90 + 102.469 + \dfrac%7B116%7D%7B4%7D \right ) + 492.5 \left ( \dfrac%7B90%7D%7B2%7D + \dfrac%7B116%7D%7B4%7D \right ) $$

Mathinline

body	--uriencoded--$$ \normalsize + 377.5 \left ( \dfrac%7B90%7D%7B2%7D + \dfrac%7B116%7D%7B2%7D \right ) +287.5(102.469) \right] + \dfrac%7B140%7D%7B2%7D = 7094.956\; \mathrm%7Bmm%7D $$

t_cf

Mathinline

body	--uriencoded--$$ \normalsize t_%7Bcf%7D \geq \sqrt%7B \dfrac %7B 1.11 M_%7Buc%7D%7D %7B\varphi F_%7Byc%7DY_c%7D %7D = \sqrt%7B \dfrac %7B 1.11 \times 861.352%7D 352\times 10%5e%7B6%7D%7D %7B 1 \times 275 \times 10%5e%7B-3%7D \times 7094.956%7D %7D = 22.137 \; \mathrm%7Bmm%7D $$

Required	Available	Ratio	Control
22.137 mm	31 mm	0.714	√

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