...
Lwı | 760 mm | AISC 360-16 J2.4(c) |
Lwt | 210 mm | |
Fe | 490 N/mm2 | |
Rnwl  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize R_%7Bnwl%7D = min ( R_%7Bnw%7D , R_%7BnBM%7D ) L_%7Bwl%7D = 2352 \times 760 \times 10%5e%7B-3%7D =1787.52\; \mathrm%7BkN%7D $$ |
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| |
Rnwt  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize R_%7Bnwt%7D = min ( R_%7Bnw%7D , R_%7BnBM%7D ) L_%7Bwt%7D = 2352 \times 210 \times 10%5e%7B-3%7D =493.92\; \mathrm%7BkN%7D $$ |
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| |
Rnw  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize R_%7Bnw%7D = 0.6 F_E 0.707 w = 0.6 \times 490 \times 0.707 \times 11.315 =2352\; \mathrm%7BkN%7D $$ |
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| |
w | 11.315 mm | |
Fu-plate | 360 N/mm2 | |
Fu-flange | 360 N/mm2 | |
tp | 16 mm | |
tf | 17.2 mm | |
RnBM  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize R_%7BnBM%7D = min ( 0.6 F_%7Bu-plate%7D \times t_p , 0.6F_%7Bu-flange%7D ) $$ |
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| Mathinline |
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| body | --uriencoded--$$ \normalsize R_%7BnBM%7D = (0.6 \times 360 \times 16; 0.6 \times 360 \times 17.2 ) = 3456\; \mathrm%7BkN%7D $$ |
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| |
Rn  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize R_%7Bn%7D = max ( R_%7Bnwl%7D + R_%7Bnwt%7D , 0.85R_%7Bnwl%7D + 1.5R_%7Bnwt%7D ) = 2281.44\; \mathrm%7BkN%7D $$ |
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| |
ΦRn  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 2281.44 = 1711.08 \; \mathrm%7BkN%7D $$ |
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| |
Required | Available | Ratio | Control |
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505.682 kN | 1140.426 kN | 0.296 | √ |
...
The limit state of tension plate yield is checked according to AISC 360-16.
Ag  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize A_%7Bg%7D = h_p t_p = 280 \times 16 = 4480 \; \mathrm%7Bmm%5e2%7D $$ |
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| |
Fy | 275 N/mm2 | |
Rn  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize R_%7Bn%7D = F_y A_g = 275 \times 10%5e%7B-3%7D \times 4480 = 1232 \; \mathrm%7BkN%7D $$ |
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|
| AISC 360-16 (J4-1) |
ΦRn  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize \varphi R_n = 0.90 \times 1232 = 1108.8 \; \mathrm%7BkN%7D $$ |
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Required | Available | Ratio | Control |
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505.682 kN | 1108.8 kN | 0.456 | √ |
...
The limit state of the flange plate tension rupture is checked according to AISC 360-16.
An  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize A_%7Bg%7D = h_p t_p = 280 \times 16 = 4480 \; \mathrm%7Bmm%5e2%7D $$ |
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| |
Ae  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize A_%7Be%7D = A_%7Bn%7D U = 4480 \times 1.0 = 4480\; \mathrm%7Bmm%5e2%7D$$ |
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Fu | 410 N/mm2 | |
U | 1.00 | |
Rn  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize R_%7Bn%7D = F_%7Bu%7D A_%7Be%7D = 410 \times 10%5e%7B-3%7D \times 4480 = 1836.8 \; \mathrm%7BkN%7D $$ |
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|
| AISC 360-16 (J4-2) |
ΦRn  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 1836.8 = 1377.6 \; \mathrm%7BkN%7D $$ |
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Required | Available | Ratio | Control |
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505.682 kN | 1377.6 kN | 0.367 | √ |
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The block shear limit state is checked according to AISC 360-16.
Ag  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize A_%7Bg%7D = 2 \times 16 \times(400 - 20) = 12160 \; \mathrm%7Bmm%5e2%7D $$ |
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Anv  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize A_%7Bnv%7D = 12160 - 0 = 12160 \; \mathrm%7Bmm%5e2%7D $$ |
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Ant  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize A_%7Bnt%7D = 210 \times 16 = 3360 \; \mathrm%7Bmm%5e2%7D $$ |
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Fy | 275 N/mm2 | |
Fu | 410 N/mm2 | |
Ubs | 1.0 | |
|  Image Removed | | Rn |  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize U_%7Bbs%7D F_u A_%7Bnt%7D = 1 \times 410 \times 10%5e%7B-3%7D \times 3360 = 1377.6 $$ |
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| Mathinline |
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| body | --uriencoded--$$ \normalsize 0.6 F_%7Bu%7D A_%7Bnv%7D = 0.6 \times 410 \times 10%5e%7B-3%7D \times 12160 = 2991.36 $$ |
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| Mathinline |
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| body | --uriencoded--$$ \normalsize 0.6 F_%7By%7D A_%7Bg%7D = 0.6 \times 275 \times 10%5e%7B-3%7D \times 12160 = 2006.4 $$ |
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Rn | | Mathinline |
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| body | --uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 0.6F_uA_%7Bnv%7D \\0.6F_yA_%7Bg%7D \end%7Bmatrix%7D\right] \end%7Baligned%7D + U_%7Bbs%7DF_uA_%7Bnt%7D |
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| Mathinline |
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| body | --uriencoded--\normalsize R_%7Bn%7D =2006.4 + 1377.6 = 3384\; \mathrm%7BkN%7D |
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|
| AISC 360-16 (J4-5) |
ΦRn  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 3384 = 2538 \; \mathrm%7BkN%7D $$ |
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Required | Available | Ratio | Control |
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505.682 kN | 2538 kN | 0.199 | √ |
...
K | 0.65 | |
L | 20 mm | |
r | 4.619 mm | |
KL / r | 2.81 | |
Fy | 275 N/mm2 | |
Ag Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize A_%7Bg%7D = h_p t_p = 280 \times 16 = 4480 \; \mathrm%7Bmm%5e2%7D $$ |
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Rn Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize R_%7Bn%7D = F_%7By%7D A_%7Bg%7D = 275 \times 10%5e%7B-3%7D \times 4480 = 1232 \; \mathrm%7BkN%7D $$ |
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|
| AISC 360-16 (J4-6) |
ΦRn Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize \varphi R_n = 0.90 \times 1232 = 1108.8 \; \mathrm%7BkN%7D $$ |
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Required | Available | Ratio | Control |
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505.682 kN | 1108.8 kN | 0.456 | √ |
...
w | 11.315 mm |
FE | 490 N/mm2 |
l | 260 mm |
e | 117.5 mm |
Rn |  Image Removed | ΦRn |  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize R_n = \dfrac%7B w l F_E %7D%7B\sqrt %7B2.25 + 12 \left ( \dfrac%7Be%7D%7Bl%7D \right )%5e2 %7D %7D = \dfrac%7B 11.315 \times 260 \times 490 \times 10%5e%7B-3%7D %7D%7B\sqrt %7B2.25 + 12 \left ( \dfrac%7B117.5%7D%7B260%7D \right )%5e2 %7D %7D =664.86 \; \mathrm%7BkN%7D $$ |
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ΦRn | | Mathinline |
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| body | --uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 664.86 = 498.65 \; \mathrm%7BkN%7D $$ |
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Required | Available | Ratio | Control |
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135.975 kN | 498.69 kN | 0.273 | √ |
...
The nominal and design strength of the weld is checked according to AISC 360-16
Fe | 490000 kN490 N/mmm2 | |
w | 11.315 mm | |
Fu | 360 N/mm2 | |
t | 11.1 mm | |
Rnw |  Image Removed | RnBM |  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize R_%7Bnw%7D = 0.6 F_E 0.707 w $$ |
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| Mathinline |
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| body | --uriencoded--$$ \normalsize R_%7Bnw%7D = 0.6 \times 490 \times 0.707 \times 11.315 \times 10%5e%7B-3%7D =2351.79 \; \mathrm%7BkN%7D $$ |
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| |
RnBM | | Mathinline |
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| body | --uriencoded--$$ \normalsize R_%7BnBM%7D = 0.6 F_u t = 0.6 \times 360 \times 11.1 =2397.6\; \mathrm%7BkN%7D $$ |
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|
| AISC Manual 14th 8-12 |
Rn  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize R_%7Bn%7D = min ( R_%7Bnw%7D , R_%7BnBM%7D ) =2351.79\; \mathrm%7BkN%7D $$ |
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| |
ΦRn |  Image Removed| body | --uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 2351.79 = 1764 \; \mathrm%7BkN%7D$$ |
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Required | Available | Ratio | Control |
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579.254 kN/m | 1764 kN/m | 0.328 | √ |
...
The nominal and design yield strength of the web plate is checked according to AISC 360-16
Ag  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize A_%7Bg%7D = L_p t_p = (260 \times 10) = 2600 \; \mathrm%7Bmm%5e2%7D $$ |
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Fy | 275 N/mm2 | |
Rn  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize R_%7Bn%7D = 0.6 F_y A_g = 0.6 \times 275 \times 10%5e%7B-3%7D \times 2600 =429\; \mathrm%7BkN%7D $$ |
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| AISC 360-16 J4-3 |
ΦRn  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize \varphi R_n = 1 \times 429 = 429 \; \mathrm%7BkN%7D $$ |
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Required | Available | Ratio | Control |
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135.975 kN | 429 kN | 0.317 | √ |
...
The limit state of the web plate shear rupture is checked according to AISC 360-16.
Anv  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize A_%7Bnv%7D = t_p (d_b - n_b d_e) = 10 \times ( 260 - 2 \times 29 ) =2020 \; \mathrm%7Bmm%5e2%7D $$ |
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Fu | 410 N/mm2 | |
Rn  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize R_%7Bn%7D = 0.6 F_u A_%7Bnv%7D = 0.6 \times 410 \times 10%5e%7B-3%7D \times 2020 =496.92 \; \mathrm%7BkN%7D $$ |
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|
| AISC 360-16 J4-3 |
ΦRn  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 496.92 = 372.69 \; \mathrm%7BkN%7D $$ |
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Required | Available | Ratio | Control |
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135.975 kN | 372.69 kN | 0.365 | √ |
...
dp | 260 mm |
Fy | 275 N/mm2 |
tp | 10 mm |
a | 117.5 mm |
Rn |  Image Removed | ΦRn |  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize R_n = \dfrac%7B F_y d_p t_p %7D%7B\sqrt %7B2.25 + 16 \left ( \dfrac%7Ba%7D%7Bd_p%7D \right )%5e2 %7D %7D = \dfrac%7B 275 \times 10%5e%7B-3%7D \times 260 \times 10 %7D%7B\sqrt %7B2.25 + 16 \left ( \dfrac%7B117.5%7D%7B260%7D \right )%5e2 %7D %7D =304.387 \; \mathrm%7BkN%7D $$ |
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|
ΦRn | | Mathinline |
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| body | --uriencoded--$$ \normalsize \varphi R_n = 0.90 \times 304.387 = 273.948 \; \mathrm%7BkN%7D $$ |
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Required | Available | Ratio | Control |
|---|
135.975 kN | 273.948 kN | 0.496 | √ |
...
Pr | 1621.397 kN | AISC 360-16 J10-9 |
Py  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize P_%7By%7D = F_y A_g = 275 \times 10%5e%7B-3%7D \times28634.759 = 7874.559 \; \mathrm%7BkN%7D $$ |
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| |
Fy | 275000 kN/m2 | |
Ag | 28634.759 mm2 | |
dc | 650 mm | |
tw | 16 mm | |
Rn  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize R_n = 0.6F_%7By%7D d_c t_w = 0.6 \times 275 \times 10%5e%7B-3%7D \times 650 \times 16 = 1716 \; \mathrm%7BkN%7D $$ |
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| |
ΦRn  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize \varphi R_n = 0.90 \times 1716 = 1544.4 \; \mathrm%7BkN%7D $$ |
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| |
Required | Available | Ratio | Control |
|---|
56.746 kN | 1544.4 kN | 0.037 | √ |
...