Page Comparison

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M_uc

796.489 kNm

AISC 358-16 (6.8-3)

F_t

750000 kN750 N/mmm²

h_o

Mathinline

body	--uriencoded--$$ \normalsize h_%7Bo%7D = d - \dfrac%7Bt_%7Bfo%7D%7D %7B2%7D + p_%7Bfo%7D = 450 - \dfrac %7B15%7D %7B2%7D + 60 = 502.5 \; \; \mathrm%7Bmm%7D $$

h₁

Mathinline

body	--uriencoded--$$ \normalsize h_%7B1%7D = d - 1.5t_%7Bfo%7D - p_%7Bfi%7D = 450 - 1.5 \times 15 - 60 = 367.5 \; \; \mathrm%7Bmm%7D $$

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--$$ \normalsize d_b \geq \sqrt%7B \dfrac %7B 2 \times 796.489%7D 489 \times 10%5e6%7D %7B0.90 \times \pi \times 750000 750 \times (502.5 + 367.5)%7D %7D =29.385 \; \; \mathrm%7Bmm%7D $$

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M_uc

796.489 kNm

AISC 358-16 (6.8-5)

F_yp

275000 kN275 N/mmm²

s

Mathinline

body	--uriencoded--$$ \normalsize s = \dfrac%7B1%7D%7B2%7D \sqrt%7B b_pg%7D = \dfrac%7B1%7D%7B2%7D \sqrt%7B 290 \times 150%7D = 104.28 $$

Y_p

Mathinline

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

Y_p

Mathinline

body	--uriencoded--$$ \small Y_p = \dfrac%7B290%7D%7B2%7D \left [ 367.5 \left ( \dfrac%7B1%7D%7B60%7D + \dfrac%7B1%7D%7B104.28%7D \right ) + 502.5 \left ( \dfrac%7B1%7D%7B60%7D \right ) - \dfrac%7B1%7D%7B2%7D \right ] + \dfrac%7B2%7D%7B150%7D [ 367.5(60 + 104.28 ) ] $$

Mathinline

body	--uriencoded--$$ \small Y_p = 3345.972\; \mathrm%7Bmm%7D $$

t_p

Mathinline

body	--uriencoded--$$ \normalsize t_p \geq \sqrt%7B \dfrac %7B 1.11 M_%7Buc%7D%7D %7B\varphi F_%7Byp%7DY_p%7D %7D = \sqrt%7B \dfrac %7B 1.11 \times 796.489%7D 489 \times 10%5e6 %7D %7B 1 \times 275000 275 \times 3345.972%7D %7D = 30.997 \; \; \mathrm%7Bmm%7D $$

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M_uc

796.489 kNm

AISC 358-16 (6.8-7)

F_f

Mathinline

body	--uriencoded--$$ \normalsize F_f = \dfrac %7BM_%7Buc%7D%7D%7Bd - t_f%7D = \dfrac %7B796.489%7D%7B450 - 15%7D 489%7D%7B(450 - 15) \times 10%5e%7B-3%7D %7D =1831.009 \; \mathrm%7BkN%7D $$

R_req = F_f / 2

Mathinline

body	--uriencoded--$$ \normalsize R_%7Breq%7D = \dfrac %7BF_f%7D%7B2%7D = \dfrac %7B1831.009%7D%7B2%7D =915.504 \; \mathrm%7BkN%7D $$

F_yp

275000 kN275 N/mmm²

b_p

290 mm

t_p

32 mm

d

450 mm

t_bf

15 mm

R_n

Mathinline

body	--uriencoded--$$ \normalsize R_n = 0.6F_%7Byp%7Db_pt_p = 0$$

Mathinline

body	--uriencoded--$$ \normalsize R_n = 0.6 \times 275000 275 \times 290 \times 32 \times 10%5e%7B-3%7D = 1531.2 \; \; \mathrm%7BkN%7D $$

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The shear rupture of the end plate is checked according to AISC 358-16 §6.8.

M_uc

915796.504 489 kNm

AISC 358-16 (6.8-7)

F_f

Mathinline

body	--uriencoded--$$ \normalsize F_f = \dfrac %7BM_%7Buc%7D%7D%7Bd - t_f%7D = \dfrac %7B796.489%7D%7B450 - 15%7D 489%7D%7B(450 - 15) \times 10%5e%7B-3%7D%7D =1831.009 \; \mathrm%7BkN%7D $$

R _req = F_f / 2

Mathinline

body	--uriencoded--$$ \normalsize R_%7Breq%7D = \dfrac %7BF_f%7D%7B2%7D = \dfrac %7B1831.009%7D%7B2%7D =915.504\; \mathrm%7BkN%7D $$

F_up

410000 kN410 N/mmm²

A_n

Mathinline

body	--uriencoded--$$ \normalsize A_%7Bn%7D = 32 \times \dfrac %7B290%7D%7B2%7D =4640 $$\; \mathrm%7Bmm%5e2%7D$$

d

450 mm

t_bf

15 mm

R_n

Mathinline

body	--uriencoded--$$ \normalsize R_n = 0.6F_%7Bup%7DA_n = 0.6 \times 410000 410 \times 4640 \times 10%5e%7B-3%7D = 1141.44 \; \mathrm%7BkN%7D $$

ΦR_n

Mathinline

body	--uriencoded--$$ \normalsize \varphi R_n = 0.9 \times 1141.44 = 1027.3 \; \; \mathrm%7BkN%7D $$

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A_b

Mathinline

body	--uriencoded--$$ \normalsize A_%7Bb%7D = \dfrac %7B \pi d%5e2%7D%7B4%7D = \dfrac %7B \pi 30%5e2%7D%7B4%7D =706.858 \; \mathrm%7Bmm%5e2%7D $$

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--$$ \normalsize R_n = F_%7Bn%7DA_b = 4 \times 450 \times 706.858 \times 10%5e%7B-3%7D = 1272.34 \; \; \mathrm%7BkN%7D $$

ΦR_n

Mathinline

body	--uriencoded--$$ \normalsize \varphi R_n = 0.90 \times 1272.34 = 1145.11 \; \; \mathrm%7BkN%7D $$

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d_h

30+3=33 mm

L_c,edge

Mathinline

body	--uriencoded--$$ \normalsize L_%7Bc,edge%7D = L_e - 0.5d_h = 85 - 0.5 \times 33 = 68.5 \; \mathrm%7Bmm%7D $$

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(68.5)(32)(410 \times 10%5e%7B-3%7D) \\2.4(30)(32)(410 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D =944.64\; \mathrm%7BkN%7D

L_c,spacing

Mathinline

body	--uriencoded--$$ \normalsize L_%7Bc,spacing%7D = s - d_h = 150 - 1.5 \times 30 = 102 $$\; \mathrm%7Bmm%7D$$

R_n-spacing

Mathinline

body	--uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2(102)(32)(410 \times 10%5e%7B-3%7D) \\2.4(30)(32)(410 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D =944.6464\; \mathrm%7BkN%7D

R_n

Mathinline

body	--uriencoded--$$ \normalsize R_n = n_e R_%7Bn-edge%7D + n_s R_%7Bn-spacing%7D = 4 \times 944.64 = 3778.56 \; \; \mathrm%7BkN%7D $$

ΦR_n

Mathinline

body	--uriencoded--$$ \normalsize \varphi R_n = 0.9 \times 3778.56 = 3400.704 \; \; \mathrm%7BkN%7D $$

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

L_c,spacing

Mathinline

body	--uriencoded--$$ \normalsize L_%7Bc,spacing%7D = s - d_h = 150 - 1.5 \times 30 = 102 $$\; \mathrm%7Bmm%7D$$

R_n-spacing

Mathinline

body	--uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2(102)(32)(410 \times 10%5e%7B-3%7D) \\2.4(30)(31)(410 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D = 915.12\; \mathrm%7BkN%7D

R_n

Mathinline

body	--uriencoded--$$ \normalsize R_n = n_e R_%7Bn-edge%7D + n_s R_%7Bn-spacing%7D = 4 \times 915.12 = 3660.48 \; \; \mathrm%7BkN%7D $$

ΦR_n

Mathinline

body	--uriencoded--$$ \normalsize \varphi R_n = 0.9 \times 3660.48 = 3294.432 \; \; \mathrm%7BkN%7D $$

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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--$$ \normalsize w \geq \dfrac %7B \varphi_t F_%7Byb%7D t_%7Bbw%7D%7D %7B2 \times \varphi \times 0.6 \times F_e \times 1.5 \times0.707%7D%7D $$

Mathinline

body	--uriencoded--$$ \normalsize = \dfrac %7B 0.9 \times 275 275000 \times 10%5e%7B-3%7D \times 9%7D %7B2 \times 0.75 \times 0.6 \times 490 490000 \times 10%5e%7B-3%7D \times 1.5 \times 0.707%7D%7D = 4.763 $$

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M_uc

796.489 kNm

AISC 358-16 (6.8-13)

F_yp

275000 kN275 N/mmm²

s

Mathinline

body	--uriencoded--$$ \normalsize s = \dfrac%7B1%7D%7B2%7D \sqrt%7B b_f g%7D = \dfrac%7B1%7D%7B2%7D \sqrt%7B 300 \times 150%7D = 106.066 \; \mathrm%7Bmm%7D $$

c

Mathinline

body	--uriencoded--$$ \normalsize c = p_%7Bfo%7D + t_%7Bfo%7D + p_%7Bfi%7D = 60 + 16 + 60 = 136\; \mathrm%7Bmm%7D $$

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--$$ \small Y_c = \dfrac%7B300%7D%7B2%7D \left [ 367.5 \left ( \dfrac%7B1%7D%7B106.066%7D \right ) + 502.5 \left ( \dfrac%7B1%7D%7B106.066%7D \right ) \right ] $$

Mathinline

body	--uriencoded--$$ \small + \dfrac%7B2%7D%7B150%7D \left [ 367.5 \left ( 106.066 + \dfrac%7B3 \times 136 %7D%7B4%7D \right ) + 502.5 \left ( 106.066 + \dfrac%7B136%7D%7B4%7D \right ) + \dfrac%7B136%5e2%7D%7B2%7D \right ] + \dfrac%7B150%7D%7B2%7D $$

Mathinline

body	--uriencoded--$$ \normalsize Y_c = 5344.209\; \mathrm%7Bmm%7D $$

t_cf

Mathinline

body	--uriencoded--$$ \normalsize t_%7Bcf%7D \geq \sqrt%7B \dfrac %7B 1.11 M_%7Buc%7D%7D %7Buc%7D %7D %7B\varphi F_%7Byc%7DY_c%7D %7D = \sqrt%7B \dfrac %7B 1.11 \times 796.489%7D %7B 1 489 \times 275 10%5e%7B6%7D%7D %7B1 \times 10%5e%7B-3%7D 275\times 5344.209%7D %7D %7D = 24.527 \; \mathrm%7Bmm%7D $$

Required	Available	Ratio	Control
24.527 mm	31 mm	0.791	√

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P_r

366.473 kN

AISC 360-16 J10-9

P_y

Mathinline

body	--uriencoded--\normalsize P_%7By%7D = F_y A_g = 275 \times 10%5e%7B-3%7D \times 28634.759 = 7874.559 \; \; \mathrm%7BkN%7D

F_y

275000 kN275 N/mmm²

A _g

28634.759 mm²

d_c

650 mm

t_w

16 mm

R_n

Mathinline

body	--uriencoded--$$ \normalsize R_n = 0.6F_%7By%7Dd_ct_w = 0.6 \times 275 \times 10%5e%7B-3%7D \times 650 \times 16 = 1716 \; \; \mathrm%7BkN%7D $$

ΦR_n

Mathinline

body	--uriencoded--$$ \normalsize \varphi R_n = 1 \times 1716 = 1716 \; \; \mathrm%7BkN%7D $$

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