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The bolt shear limit state of the connection is checked according to AISC 360-16.

Ab Image Removed	Mathinline body --uriencoded--$$ \normalsize A_b = \dfrac%7B \pi d%5e2%7D %7B4%7D = \dfrac%7B \pi 20%5e2%7D %7B4%7D = 314.159 $$
Fn	Image Removed	Rn	Image Removed	Mathinline body --uriencoded--$$ \normalsize F_n = 0.450 F_%7Bub%7D = 0.450 \times 1000 =450 $$
Rn	Mathinline body --uriencoded--$$ \normalsize R_n = F_n A_b = 2 \times 450 \times 314.159 \times 10%5e%7B-3%7D =282.743 $$	AISC 360-16 J3-1
ΦRn Image Removed	Mathinline body $$ \normalsize \varphi R_n = 0.75 \times 282.743 = 212.058 $$

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The bearing strength limit states of the connection plate, which are “shear tear out” and “ovalization of bolt hole” for both end and inner bolts, are checked according to AISC 360-16.

dh	20+2=22 mm
Lc,edge Image Removed	Mathinline body --uriencoded--$$ \normalsize L_%7Bc,edge%7D = L_e - 0.5d_h = 45 - 0.5 \times 22 =34 $$
Rn Image Removed	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 360-16 J3-6a
Rn-edge Image Removed	Mathinline body --uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2(34)(15)(469.999 \times 10%5e%7B-3%7D) \\2.4(20)(15)(469.999 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D =287.64
Lc,spacing Image Removed	Mathinline body --uriencoded--$$ \normalsize L_%7Bc,spacing%7D = s - d_h = 60 - 22 =38 $$
Rn-spacing	Image Removed		Rn	Image Removed Mathinline body --uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2(38)(15)(469.999 \times 10%5e%7B-3%7D) \\2.4(20)(15)(469.999 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D =321.48
Rn	Mathinline body --uriencoded--$$ \normalsize R_%7Bn%7D = n_eR_%7Bn,edge%7D + n_sR_%7Bn,spacing%7D $$ Mathinline body --uriencoded--$$ \normalsize R_%7Bn%7D = 1 \times 287.64 + 1 \times 321.48 = 609.12 \; $$
ΦRn Image Removed	Mathinline body $$ \normalsize \varphi R_n = 0.75 \times 609.12 = 456.84 $$

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The bearing strength limit states of the connection plate, which are “shear tear out” and “ovalization of bolt hole” for both end and inner bolts, are checked according to AISC 360-16.

dh	20+2=22 mm
Lc,edge Image Removed	Mathinline body --uriencoded--$$ \normalsize L_%7Bc,edge%7D = L_e - 0.5d_h = 45 - 0.5 \times 22 = 34 $$
Rn Image Removed	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 360-16 J3-6a
Rn-edge Image Removed	Mathinline body --uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2(34)(10)(469.999 \times 10%5e%7B-3%7D) \\2.4(20)(10)(469.999 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D =191.76
Lc,spacing Image Removed	Mathinline body --uriencoded--$$ \normalsize L_%7Bc,spacing%7D = s - d_h = 60 - 22 =38 $$
Rn-spacing Image Removed	Mathinline body --uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2(38)(10)(469.999 \times 10%5e%7B-3%7D) \\2.4(20)(10)(469.999 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D =214.32
Rn Image Removed	Mathinline body --uriencoded--$$ \normalsize R_%7Bn%7D = n_eR_%7Bn,edge%7D + n_sR_%7Bn,spacing%7D $$ Mathinline body --uriencoded--$$ \normalsize R_%7Bn%7D = 1 \times 191.76 + 1 \times 214.32 = 406.08 \; $$
ΦRn Image Removed	Mathinline body $$ \normalsize \varphi R_n = 0.75 \times 406.08 = 304.56 $$

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Fe	490000 kN/m2
w	5.658 mm
Fu-plate	469.999  N/mm2
Fu-brace	410 N/mm2
tplate	15 mm	AISC 360-16 J3-6a
tbrace	15 mm
lw	150 mm
Rnw Image Removed	Mathinline body --uriencoded--$$ \normalsize R_%7Bnw%7D = 0.6 \times F_%7Be%7D \times 2 \times 0.707 \times w $$ Mathinline body --uriencoded--$$ \normalsize R_%7Bnw%7D =0.6 \times 490 \times 2 \times 2 \times 0.707 \times 5.658 = 4704 $$
Rn-plate Image Removed	Mathinline body --uriencoded--$$ \normalsize R_%7Bn,plate%7D = 0.6 F_%7Bu%7D t l = 0.6 \times 2 \times469.999 \times 15 =8460 $$
RnBM	Image Removed	Rn	Image Removed	ΦRn	Image Removed	Mathinline body --uriencoded--$$ \normalsize R_n = \mathrm%7Bmin%7D ( R_%7Bn,plate%7D , R_%7Bn,brace%7D ) =8460 $$
Rn	Mathinline body --uriencoded--$$ \normalsize R_n = \mathrm%7Bmin%7D ( R_%7Bnw%7D , R_%7BnBM%7D )l =4704 \times 150 =705.6 $$
ΦRn	Mathinline body $$ \normalsize \varphi R_n = 0.75 \times 705.6 = 529.2 $$

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K	0.65
L	0 mm
r	2.887 mm
KL / r	0
Fy	355 N/mm2
Ag	1292.82 mm2
Rn Image Removed	Mathinline body $$ \normalsize R_n = F_y A_g = 355 \times 1292.82 =458.95 $$	AISC 360-16 J4-6
ΦRn Image Removed	Mathinline body $$ \normalsize \varphi R_n = 0.90 \times 458.95 = 413.056 $$

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