...
Ab | | Mathinline |
|---|
| body | --uriencoded--$$ \normalsize A_b = \dfrac%7B \pi d%5e2%7D %7B4%7D = \dfrac%7B \pi 20%5e2%7D %7B4%7D = 314.159\; \mathrm%7Bmm%5e2%7D $$ |
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| |
Fn | | Mathinline |
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| body | --uriencoded--$$ \normalsize F_n = 0.450 F_%7Bub%7D = 0.450 \times 1000 =450\; \mathrm%7BN/mm%5e2%7D $$ |
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|
| |
Rn | | Mathinline |
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| body | --uriencoded--$$ \normalsize R_n = F_n A_b = 4 \times 450 \times 314.159 \times 10%5e%7B-3%7D = 565.486 \; \mathrm%7BkN%7D $$ |
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|
| AISC 360-16 J3-1 |
ΦRn | | Mathinline |
|---|
| body | --uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 565.486 = 424.115 \; \mathrm%7BkN%7D $$ |
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|
| |
Required | Available | Ratio | Control |
|---|
413.063 kN | 424.115 kN | 0.974 | √ |
...
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 |
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| body | --uriencoded--$$ \normalsize L_%7Bc,edge%7D = L_e - 0.5d_h = 40 - 0.5 \times 22 =29\; \mathrm%7Bmm%7D $$ |
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|
| |
Rn  Image Removed | | Mathinline |
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| 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 |
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|
| AISC 360-16 J3-6a |
Rn-edge  Image Removed | | Mathinline |
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| body | --uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2(29)(16)(470 \times 10%5e%7B-3%7D) \\2.4(20)(16)(470 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D =261.696\; \mathrm%7BkN%7D |
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|
| |
Lc,spacing  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize L_%7Bc,spacing%7D = s - d_h = 60 - 22 = 38\; \mathrm%7Bmm%7D $$ |
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|
| |
Rn-spacing  Image Removed | | Mathinline |
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| body | --uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2(38)(16)(470 \times 10%5e%7B-3%7D) \\2.4(20)(16)(470 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D =342.912\; \mathrm%7BkN%7D |
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|
| |
Rn | | Mathinline |
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| body | --uriencoded--$$ \normalsize R_%7Bn%7D = n |
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|
 Image Removed| _eR_%7Bn,edge%7D + n_sR_%7Bn,spacing%7D $$ |
|
| Mathinline |
|---|
| body | --uriencoded--$$ \normalsize R_%7Bn%7D = 2 \times 261.696 + 2 \times 342.912 = 1209.216 \; \mathrm%7BkN%7D $$ |
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|
| |
ΦRn  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 1209.216 = 906.912 \; \mathrm%7BkN%7D $$ |
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|
| |
Required | Available | Ratio | Control |
|---|
413.063 kN | 906.912 kN | 0.455 | √ |
...
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--$$ \normalsize L_%7Bc,edge%7D = L_e - 0.5d_h = 40 - 0.5 \times 22 =29 \; \mathrm%7Bmm%7D $$ |
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|
| |
Rn Image Removed | | Mathinline |
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| 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 |
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|
| 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(29)(10)(470 \times 10%5e%7B-3%7D) \\2.4(20)(10)(470 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D =163.559\; \mathrm%7BkN%7D |
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|
| |
Lc,spacing Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize L_%7Bc,spacing%7D = s - d_h = 60 - 22 = 38\; \mathrm%7Bmm%7D $$ |
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|
| |
Rn-spacing |  Image Removed | | Rn |  Image Removed | | Mathinline |
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| body | --uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2(38)(10)(470 \times 10%5e%7B-3%7D) \\2.4(20)(10)(470 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D = 214.32 \; \mathrm%7BkN%7D |
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| |
Rn | | Mathinline |
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| body | --uriencoded--$$ \normalsize R_%7Bn%7D = n_eR_%7Bn,edge%7D + n_sR_%7Bn,spacing%7D $$ |
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|
| Mathinline |
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| body | --uriencoded--$$ \normalsize R_%7Bn%7D = 2 \times 163.559 + 2 \times 214.32 = 755.758 \; \mathrm%7BkN%7D $$ |
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| |
ΦRn  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 755.758 = 566.82 \; \mathrm%7BkN%7D $$ |
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|
| |
Required | Available | Ratio | Control |
|---|
413.063 kN | 566.82 kN | 0.729 | √ |
...
Fe | 490000 kN/m2 | |
w | 5.658 mm | |
Fu-plate | 469.999 N/mm2 | |
Fu-brace | 410 N/mm2 | |
tplate | 16 mm | |
tbrace | 10 mm | |
Rnw  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize R_%7Bnw%7D = 0.6 \times F_e \times 2 \times 0.707 \times w $$ |
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|
| Mathinline |
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| body | --uriencoded--$$ \normalsize R_%7Bnw%7D = 0.6 \times 490 \times 2 \times 2 \times 0.707 \times 5.658 =4704 \; \mathrm%7BkN/m%7D $$ |
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| |
Rn-plate  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize R_%7Bn,plate%7D = 0.6 F_u t l = 0.6 \times 2 \times 469.999 \times 16 =9024\; \mathrm%7BkN/m%7D $$ |
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| |
Rn-brace |  Image Removed | RnBM |  Image Removed | Rn |  Image Removed | ΦRn |  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize R_%7Bn,brace%7D = 0.6 F_u t l = 0.6 \times 4 \times 410 \times 9.3 = 9151.2\; \mathrm%7BkN/m%7D $$ |
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|
| |
RnBM | | Mathinline |
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| body | --uriencoded--$$ \normalsize R_%7BnBM%7D = \mathrm%7Bmin%7D ( R_%7Bn,plate%7D , R_%7Bn,brace%7D ) =9024\; \mathrm%7BkN/m%7D $$ |
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| |
Rn | | Mathinline |
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| body | --uriencoded--$$ \normalsize R_%7Bn%7D = \mathrm%7Bmin%7D ( R_%7Bnw%7D , R_%7BnBM%7D )l =4704 \times 140 \times 10%5e%7B-3%7D =658.56\; \mathrm%7BkN%7D $$ |
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|
| |
ΦRn | | Mathinline |
|---|
| body | --uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 658.56 = 493.92 \; \mathrm%7BkN%7D $$ |
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|
| |
Required | Available | Ratio | Control |
|---|
413.063 kN | 493.92 kN | 0.836 | √ |
...
K | 0.65 | |
L | 159.85 mm | |
r | 2.887 mm | |
KL / r | 35.99 | |
Fy | 355 N/mm2 | |
Ag | 1892.82 mm2 | |
Fe  Image Removed | | Mathinline |
|---|
| body | --uriencoded--$$ \normalsize F_e = \dfrac%7B \pi%5e2 E%7D %7B \left ( \dfrac%7B KL%7D %7Br%7D \right)%5e2%7D = 1523692.915 \; \mathrm%7BkN/m%5e2%7D $$ |
|---|
|
| AISC 360-16 E3-4 |
|  Image Removed | |  Image Removed | | Mathinline |
|---|
| body | --uriencoded--$$ \normalsize \dfrac%7B L_c%7D %7Bi%7D \leq 4.71 \sqrt %7B\dfrac%7BE%7D%7BF_y%7D %7D $$ |
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|
| |
| | Mathinline |
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| body | --uriencoded--$$ \normalsize 34.56 \leq 4.71 \sqrt %7B\dfrac%7B 2 \times 10%5e8%7D%7B355000%7D %7D =111.8 $$ |
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|
| |
Fcr  Image Removed | | Mathinline |
|---|
| body | --uriencoded--$$ \normalsize F_%7Bcr%7D = \left[ 0.658%5e%7B\dfrac%7BF_y%7D%7BF_e%7D%7D \right ] F_y = 322.016 \; \mathrm%7BN/mm%5e2%7D $$ |
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|
| AISC 360-16 E3-2 |
Rn  Image Removed | | Mathinline |
|---|
| body | --uriencoded--$$ \normalsize R_n = F_%7Bcr%7D A_g = 322.016 \times 1892.82 \times 10%5e%7B-3%7D = 609.52 \; \mathrm%7BkN%7D $$ |
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|
| AISC 360-16 E3-1 |
ΦRn  Image Removed | | Mathinline |
|---|
| body | --uriencoded--$$ \normalsize \varphi R_n = 0.9 \times 609.52 = 548.567 \; \mathrm%7BkN%7D $$ |
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|
| |
Required | Available | Ratio | Control |
|---|
413.063 kN | 548.567 kN | 0.753 | √ |
...
K | 0.65 | |
L | 60 mm | |
r | 4.619 mm | |
KL / r | 8.44 | |
Fy | 355 N/mm2 | |
Ag | 3195.199 mm2 | |
Rn  Image Removed | | Mathinline |
|---|
| body | --uriencoded--$$ \normalsize R_n = F_%7By%7D A_%7Bg%7D (KL / r \leq 25 ) = 355 \times 3195.199 \times 10%5e%7B-3%7D = 1134.3 \; \mathrm%7BkN%7D $$ |
|---|
|
| AISC 360-16 J4-6 |
ΦRn  Image Removed | | Mathinline |
|---|
| body | --uriencoded--$$ \normalsize \varphi R_n = 0.9 \times 1134.3 = 1020.866\; \mathrm%7BkN%7D $$ |
|---|
|
| |
Required | Available | Ratio | Control |
|---|
413.063 kN | 1020.866 kN | 0.405 | √ |
...
The yield limit state of the connection gusset plate subjected to axial force is checked according to AISC 360-16.
Fy | 355 N/mm2 |
Zg |  Image Removed | Fa |  Image Removed| Mathinline |
|---|
| body | --uriencoded--$$ \normalsize Z_g = \dfrac%7B t_%7Bgl%7D - g%5e2 %7D %7B 4%7D = 333500.966 $$ |
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|
|
Fa | | Mathinline |
|---|
| body | --uriencoded--$$ \normalsize F_a = N/ ( t_g l_g ) = 292.08 / ( 10 \times 365.24 ) = 79969.3\; \mathrm%7BkN/m%5e2%7D $$ |
|---|
|
|
N | 260,207 kN |
M | 10.775 kNm |
tg | 10 mm |
lg | 365.24 mm |
Fb |  Image Removed |
Fn |  Image Removed |
Rn |  Image Removed |
ΦRn |  Image Removed | | Mathinline |
|---|
| body | --uriencoded--$$ \normalsize F_b = M/ Z_g = 12.095 / 333500.966 = 36267.78 \; \mathrm%7BkN/m%5e2%7D $$ |
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|
|
Fn | | Mathinline |
|---|
| body | --uriencoded--$$ \normalsize F_n = F_a + F_b = 116237.092 \; \mathrm%7BkN/m%5e2%7D $$ |
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|
|
Rn | | Mathinline |
|---|
| body | --uriencoded--$$ \normalsize R_n = F_y = 355000 \; \mathrm%7BkN/m%5e2%7D $$ |
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|
|
ΦRn | | Mathinline |
|---|
| body | --uriencoded--$$ \normalsize \varphi R_n = 0.90 \times 355000 = 319500 \; \mathrm%7BkN/m%5e2%7D $$ |
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|
|
Required | Available | Ratio | Control |
|---|
116237.092 kN/m2 | 319500 kN/m2 | 0.364 | √ |
...
Fy | 355 N/mm2 |
V | 292.079 kN |
tg | 10 mm |
lg | 365.24 mm |
Fv  Image Removed | | Mathinline |
|---|
| body | --uriencoded--$$ \normalsize F_v = V/ (t_g l_g ) = 292.079/ ( 10 \times 365.24 ) = 79969.06 \; \mathrm%7BkN/m%5e2%7D $$ |
|---|
|
|
Rn  Image Removed | | Mathinline |
|---|
| body | --uriencoded--$$ \normalsize R_n = 0.6 F_y = 0.6 \times 355000 = 213000 \; \mathrm%7BkN/m%5e2%7D$$ |
|---|
|
|
ΦRn  Image Removed | | Mathinline |
|---|
| body | --uriencoded--$$ \normalsize \varphi R_n = 1.0 \times 355000 = 355000 \; \mathrm%7BkN/m%5e2%7D $$ |
|---|
|
|
Required | Available | Ratio | Control |
|---|
79969.139 kN/m2 | 213000 kN/m2 | 0.375 | √ |
Weld Strength
Fpeak  Image Removed | | Mathinline |
|---|
| body | --uriencoded--$$ \normalsize F_%7Bpeak%7D = t_g \sqrt%7B (F_a + F_b)%5e2 + F_v%5e2 %7D $$ |
|---|
|
| Mathinline |
|---|
| body | --uriencoded--$$ \normalsize F_%7Bpeak%7D = 10 \sqrt%7B (79969.307 + 36267.786)%5e2 + 79969.139%5e2 %7D $$ |
|---|
|
| Mathinline |
|---|
| body | --uriencoded--$$ \normalsize F_%7Bpeak%7D = 1410.891 \; \mathrm%7BkN/m%7D $$ |
|---|
|
| |
Favg  Image Removed | | Mathinline |
|---|
| body | --uriencoded--$$ \normalsize F_%7Bavg%7D = \dfrac %7B t_g \sqrt%7B (F_a - F_b)%5e2 + F_v%5e2%7D + \sqrt%7B (F_a + F_b)%5e2 + F_v%5e2 %7D %7D%7B 2 %7D =1161.101\; \mathrm%7BkN/m%7D $$ |
|---|
|
| |
Rreq  Image Removed | | Mathinline |
|---|
| body | --uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 3231.396 = 2423.547\; \mathrm%7BkN/m%7D $$ |
|---|
|
| AISC 360-16 J2-4 |
tg | 10 mm | |
w | 5.658 mm | |
Fe | 490000 kN/m2 | |
θ | 55.473 ° | |
Rn  Image Removed | | Mathinline |
|---|
| body | --uriencoded--$$ \normalsize R_n = 2 \times 0.707 w \times 0.6 F_E (1 + 0.5 sin (\phi)%5e%7B1.5%7D ) = 3231.396\; \mathrm%7BkN/m%7D $$ |
|---|
|
| |
ΦRn Image Removed | | Mathinline |
|---|
| body | --uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 3231.396 = 2423.547 \; \mathrm%7BkN/m%7D $$ |
|---|
|
| |
Required | Available | Ratio | Control |
|---|
1451.376 kN/m | 2423.547 kN/m | 0.599 | √ |
...