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Bolt tensile strength is checked due to axial force and bending moment interaction effect.
Ft | 750000 kN/m2 | |
Ab Image Removed | Mathinline |
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body | --uriencoded--$$ \normalsize A_b = \dfrac%7B \pi d%5e2%7D %7B4%7D = \dfrac%7B \pi 24%5e2%7D %7B4%7D = 452.389 \; \mathrm%7Bmm%5e2%7D $$ |
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| AISC DG-4-2nd 3.7 |
Pt Image Removed | Mathinline |
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body | --uriencoded--$$ \normalsize P_t = F_%7Bt%7DA_b = 750 \times 10%5e%7B-3%7D \times 452.389 = 339.292 $$ |
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| |
h0 | 473.038 mm | |
h1 | 315.271 mm | |
dm | 394.154 mm | |
Mreq | 119.655 kNm | |
Nreq | -27.504 kN | |
Rreq | Image Removed | | Rn | Image Removed Mathinline |
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body | --uriencoded--$$ \normalsize R_%7Breq%7D = \dfrac%7B M_%7Breq%7D %7D%7Bd_m%7D + \dfrac%7B N_%7Breq%7D %7D%7B2%7D = \dfrac%7B 119.655 %7D%7B394.154 \times 10%5e%7B-3%7D %7D + \dfrac%7B -27.504 %7D%7B2%7D = 289.822 \; \mathrm%7BkN%7D $$ |
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Rn | Mathinline |
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body | --uriencoded--$$ \normalsize R_n = \dfrac%7B 2 P_t ( h_o + h_1 ) %7D%7B d_m %7D $$ |
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Mathinline |
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body | --uriencoded--$$ \normalsize R_n = \dfrac%7B 2 \times 339.292 \times (473.038 + 315.271 ) %7D%7B 394.154 %7D =1357.17 \; \mathrm%7BkN%7D $$ |
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body | --uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 1357.17 = 1017.876\; \mathrm%7BkN%7D $$ |
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Required | Available | Ratio | Control |
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289.822 kN | 1017.876 kN | 0.285 | √ |
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The required end plate thickness, tp, for four bolts stiffened end plate connection is checked according to AISC 358-16 §6.8
Ab Image Removed | Mathinline |
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body | --uriencoded--$$ \normalsize A_b = \dfrac%7B \pi d%5e2%7D %7B4%7D = \dfrac%7B \pi 24%5e2%7D %7B4%7D = 452.389 \; \mathrm%7Bmm%5e2%7D $$ |
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Pt Image Removed | Mathinline |
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body | --uriencoded--$$ \normalsize P_t = F_%7Bt%7DA_b = 750 \times 10%5e%7B-3%7D \times 452.389 = 339.292 \; \mathrm%7BkN%7D $$ |
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Mn Image Removed | Mathinline |
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body | $$ \normalsize M_n = 2 P_t ( h_o + h_1 ) $$ |
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Mathinline |
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body | --uriencoded--$$ \normalsize M_n = 2 \times 339.292 ( 473.038 + 315.271 ) \times10%5e%7B-3%7D = 534.934 \; \mathrm%7BkNm%7D $$ |
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| AISC 358-16 (6.8-5) |
Fyp | 235000 kN/m2 | |
Yp | 2517.347 mm | |
tp Image Removed | Mathinline |
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body | --uriencoded--$$ \normalsize t_%7Breq%7D = \sqrt%7B \dfrac%7B 1.11 \varphi M_n %7D %7B \varphi F_%7Byp%7D Y_p %7D %7D =\sqrt%7B \dfrac%7B 1.11 \times 0.75 \times 534.934 \times10%5e6 %7D %7B 0.9 \times 235 \times 2517.347 %7D %7D =28.921 $$ |
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Required | Available | Ratio | Control |
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28.921 mm | 30 mm | 0.964 | √ |
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The shear strength of connecting elements in shear is the minimum value obtained according to the limit states of shear yielding and shear rupture. Shear yielding is checked according to AISC 360-16.
Fyp | 235000 kN/m2 | |
Ag Image Removed | Mathinline |
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body | --uriencoded--$$ \normalsize A_%7Bg%7D = L_p \times t_ p = 420 \times 30 =12600 \; \; \mathrm%7Bmm%5e2%7D $$ |
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| AISC 360-16 J4-3 |
dm | 394.154 mm | |
Mreq | 119.655 kNm | |
Nreq | -27.504 kN | |
Rreq Image Removed | Mathinline |
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body | --uriencoded--$$ \normalsize R_%7Breq%7D = \dfrac%7B M_%7Breq%7D %7D%7Bd_m%7D + \dfrac%7B N_%7Breq%7D %7D%7B2%7D = \dfrac%7B 119.655 %7D%7B394.154 \times 10%5e%7B-3%7D %7D + \dfrac%7B -27.504 %7D%7B2%7D = 289.822 \; \mathrm%7BkNm%7D $$ |
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body | $$ \normalsize R_n = 0.6 F_y A_g = 0.6 \times 235 \times 12600 = 1776.6 $$ |
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body | $$ \normalsize \varphi R_n = 1 \times 1776.6 = 1776.6 $$ |
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Required | Available | Ratio | Control |
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289.822 kN | 1776.6 kN | 0.163 | √ |
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The shear strength of connecting elements in shear is the minimum value obtained according to the limit states of shear yielding and shear rupture. Shear rupture is checked according to AISC 360-16.
Fu | 360000 kN/m2 | |
An Image Removed | Mathinline |
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body | --uriencoded--$$ \normalsize A_%7Bn%7D = 30 ( 420 - 4 \times ( 24 + 2 + 3 ) ) =9120 \; \mathrm%7Bmm%5e2%7D $$ |
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| AISC 360-16 J4-4 |
dm | 394.154 mm | |
Mreq | 119.655 kNm | |
Nreq | -27.504 kN | |
Rreq Image Removed | Mathinline |
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body | --uriencoded--$$ \normalsize R_%7Breq%7D = \dfrac%7B M_%7Breq%7D %7D%7Bd_m%7D + \dfrac%7B N_%7Breq%7D %7D%7B2%7D = \dfrac%7B 119.655 %7D%7B394.154 \times 10%5e%7B-3%7D %7D + \dfrac%7B -27.504 %7D%7B2%7D = 289.822 \; \mathrm%7BkNm%7D $$ |
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Rn Image Removed | Mathinline |
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body | --uriencoded--$$ \normalsize R_n = 0.6 F_u A_n = 0.6 \times 360 \times 9120 = 1969.92\; \mathrm%7BkN%7D $$ |
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ΦRn Image Removed | Mathinline |
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body | --uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 1969.92 = 1477.44\; \mathrm%7BkN%7D $$ |
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Required | Available | Ratio | Control |
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289.822 kN | 1477.44 kN | 0.196 | √ |
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The calculation is made using the Elastic method, one of the methods selected in the steel analysis settings tab. For the details of this check, AISC Manual 14th 7-8 is used as a reference. In this check, the operation is performed on half of the symmetry axis and is calculated to form a force pair with the required force.
Ab Image Removed | Mathinline |
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body | --uriencoded--$$ \normalsize A_b = \dfrac%7B \pi d%5e2%7D %7B4%7D = \dfrac%7B \pi 24%5e2%7D %7B4%7D = 452.389\; \mathrm%7Bmm%5e2%7D $$ |
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Fnv Image Removed | 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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body | --uriencoded--$$ \normalsize R_n = F_n A_b = 4 \times 450 \times 452.389 \times 10%5e%7B-3%7D = 814.3\; \mathrm%7BkN%7D $$ |
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| AISC 360-16 J3-1 |
ΦRn Image Removed | Mathinline |
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body | --uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 814.3 = 610.725 \; \; \mathrm%7BkN%7D $$ |
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Required | Available | Ratio | Control |
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5.313 kN | 610,725 kN | 0.009 | √ |
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Bearing strength limit states of the connection plate that are “shear tear out” and “ovalization of bolt hole” for both end and inner bolts are checked according to AISC 360-16.
dh | 24+3=27 mm | |
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body | --uriencoded--$$ \normalsize L_%7Bc,edge%7D = L_e - 0.5d_h = 51.519 - 0.5 \times 27 = 38.019\; \mathrm%7Bmm%7D $$ |
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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 |
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body | --uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2(38.019)(30)(360 \times 10%5e%7B-3%7D) \\2.4(24)(30)(360\times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D =492.72\; \mathrm%7BkN%7D |
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Lc,spacing Image Removed | Mathinline |
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body | --uriencoded--$$ \normalsize L_%7Bc,spacing%7D =157.767 - 27 = 130.767\; \mathrm%7Bmm%7D $$ |
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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(130.767)(30)(360 \times 10%5e%7B-3%7D) \\2.4(24)(30)(360\times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D =622.08\; \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--$$ \normalsize R_%7Bn%7D = 2 \times 492.72 + 2 \times 622.08 = 2229.6 \; \mathrm%7BkN%7D $$ |
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ΦRn Image Removed | Mathinline |
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body | --uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 2229.6 = 1672.2\; \mathrm%7BkN%7D $$ |
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Required | Available | Ratio | Control |
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5.313 kN | 1672.2kN | 0.003 | √ |
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Fyp | 235000 kN/m2 | AISC DG-4-2 nd 2.1.7 |
tbw | 9 mm | |
Fe | 480000 kN/m2 | |
w Image Removed | Mathinline |
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body | --uriencoded--$$ \normalsize w \geq \dfrac %7B \varphi 0.6 F_%7Byp%7D t_%7Bwb%7D%7D %7B2 \varphi_w 0.6 F_e 0.707%7D%7D =\dfrac %7B 1 \times 0.6 \times 235 \times 9%7D %7B2 \times 0.75 \times 0.6 \times 480\times 0.707%7D%7D = 3.97\; \mathrm%7Bmm%7D $$ |
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Required | Available | Ratio | Control |
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3.97 mm | 8.487 mm | 0.468 | √ |
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w | 8.487 mm | |
FE | 480 N/mm2 | |
le | 190.193 mm | |
Rn Image Removed | Mathinline |
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body | --uriencoded--$$ \normalsize R_n = 2 \times 0.6 \times 480 \times 10%5e%7B-3%7D \times 0.707 \times 8.487 \times 190.193 = 657.34\; \mathrm%7BkN%7D $$ |
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|
| AISC DG-4-2 nd 2.1.8 |
ΦRn Image Removed | Mathinline |
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body | --uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 657.34 = 493\; \mathrm%7BkN%7D $$ |
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Required | Available | Ratio | Control |
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5.313 kN | 492.981 kN | 0.011 | √ |
...