Page Comparison

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Symbols

A_b: Non-threaded bolt web characteristic cross-sectional area
A_g: Gross area
A_n: Net cross-section area
d: Characteristic diameter of the stem of the bolt (the diameter of the non-threaded stem of the bolt)
d_h: Bolt hole diameter
F_y: Structural steel characteristic yield strength
F_u: Structural steel characteristic tensile strength
F_yb: Bolt characteristic yield strength
F_ub: Bolt characteristic tensile strength
s: Distance between bolt-holecenters
L_c: The clear distance between bolt holes
L_e: The distance from the center of the bolt hole to the edge of the assembled element
L_eh: The horizontal distance from the center of the bolt hole to the edge of the assembled element
L_ev: The vertical distance from the center of the bolt hole to the edge of the assembled element
t_p: Plate thickness
P_t: Bolt tensile strength
R_n: Characteristic strength
w: Size of weld leg, in. (mm)

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Connection Geometry

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GEOMETRY CHECKS

Horizontal Edge Distance

The distance from the center of the hole to the edge of the connected part in the horizontal direction is checked per AISC 360-16.

Vertical Edge Distance

The distance from the center of the hole to the edge of the connected part in the vertical direction is checked per AISC 360-16.

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Weld Size

The minimum size of fillet welds is checked according to AISC 360-16 Table J2.4

STRENGTH CHECKS

Bolt Tension at Support

Bolt tensile strength is checked due to axial force and bending moment interaction effect.

Ft	750000 kN/m2
Ab Image Removed	Mathinline body --uriencoded--$$ \normalsize A_b = \dfrac%7B \pi d%5e2%7D %7B4%7D = \dfrac%7B \pi 24%5e2%7D %7B4%7D = 452.389 \; \mathrm%7Bmm%5e2%7D $$	AISC DG-4-2nd 3.7
Pt Image Removed	Mathinline body --uriencoded--$$ \normalsize P_t = F_%7Bt%7DA_b = 750 \times 10%5e%7B-3%7D \times 452.389 = 339.292 $$
h0	473.038 mm
h1	315.271 mm
dm	394.154 mm
Mreq	119.655 kNm
Nreq	-27.504 kN
Rreq Image Removed	Mathinline body --uriencoded--$$ \normalsize R_%7Breq%7D = \dfrac%7B M_%7Breq%7D %7D%7Bd_m%7D + \dfrac%7B N_%7Breq%7D %7D%7B2%7D = \dfrac%7B 119.655 %7D%7B394.154 \times 10%5e%7B-3%7D %7D + \dfrac%7B -27.504 %7D%7B2%7D = 289.822 \; \mathrm%7BkN%7D $$
Rn Image Removed	Mathinline body --uriencoded--$$ \normalsize R_n = \dfrac%7B 2 P_t ( h_o + h_1 ) %7D%7B d_m %7D $$ Mathinline body --uriencoded--$$ \normalsize R_n = \dfrac%7B 2 \times 339.292 \times (473.038 + 315.271 ) %7D%7B 394.154 %7D =1357.17 \; \mathrm%7BkN%7D $$
ΦRn Image Removed	Mathinline body --uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 1357.17 = 1017.876\; \mathrm%7BkN%7D $$

End Plate Thickness

The required end plate thickness, t_p, for four bolts stiffened end plate connection is checked according to AISC 358-16 §6.8

Ab Image Removed	Mathinline body --uriencoded--$$ \normalsize A_b = \dfrac%7B \pi d%5e2%7D %7B4%7D = \dfrac%7B \pi 24%5e2%7D %7B4%7D = 452.389 \; \mathrm%7Bmm%5e2%7D $$
Pt Image Removed	Mathinline body --uriencoded--$$ \normalsize P_t = F_%7Bt%7DA_b = 750 \times 10%5e%7B-3%7D \times 452.389 = 339.292 \; \mathrm%7BkN%7D $$
Mn Image Removed	Mathinline body $$ \normalsize M_n = 2 P_t ( h_o + h_1 ) $$ Mathinline body --uriencoded--$$ \normalsize M_n = 2 \times 339.292 ( 473.038 + 315.271 ) \times10%5e%7B-3%7D = 534.934 \; \mathrm%7BkNm%7D $$	AISC 358-16 (6.8-5)
Fyp	235000 kN/m2
Yp	2517.347 mm
tp Image Removed	Mathinline body --uriencoded--$$ \normalsize t_%7Breq%7D = \sqrt%7B \dfrac%7B 1.11 \varphi M_n %7D %7B \varphi F_%7Byp%7D Y_p %7D %7D =\sqrt%7B \dfrac%7B 1.11 \times 0.75 \times 534.934 \times10%5e6 %7D %7B 0.9 \times 235 \times 2517.347 %7D %7D =28.921 $$

End Plate Shear Yield

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 body --uriencoded--$$ \normalsize A_%7Bg%7D = L_p \times t_ p = 420 \times 30 =12600 \; \; \mathrm%7Bmm%5e2%7D $$	AISC 360-16 J4-3
dm	394.154 mm
Mreq	119.655 kNm
Nreq	-27.504 kN
Rreq Image Removed	Mathinline body --uriencoded--$$ \normalsize R_%7Breq%7D = \dfrac%7B M_%7Breq%7D %7D%7Bd_m%7D + \dfrac%7B N_%7Breq%7D %7D%7B2%7D = \dfrac%7B 119.655 %7D%7B394.154 \times 10%5e%7B-3%7D %7D + \dfrac%7B -27.504 %7D%7B2%7D = 289.822 \; \mathrm%7BkNm%7D $$
Rn Image Removed	Mathinline body $$ \normalsize R_n = 0.6 F_y A_g = 0.6 \times 235 \times 12600 = 1776.6 $$
ΦRn Image Removed	Mathinline body $$ \normalsize \varphi R_n = 1 \times 1776.6 = 1776.6 $$

End Plate Shear Rupture

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 body --uriencoded--$$ \normalsize A_%7Bn%7D = 30 ( 420 - 4 \times ( 24 + 2 + 3 ) ) =9120 \; \mathrm%7Bmm%5e2%7D $$	AISC 360-16 J4-4
dm	394.154 mm
Mreq	119.655 kNm
Nreq	-27.504 kN
Rreq Image Removed	Mathinline body --uriencoded--$$ \normalsize R_%7Breq%7D = \dfrac%7B M_%7Breq%7D %7D%7Bd_m%7D + \dfrac%7B N_%7Breq%7D %7D%7B2%7D = \dfrac%7B 119.655 %7D%7B394.154 \times 10%5e%7B-3%7D %7D + \dfrac%7B -27.504 %7D%7B2%7D = 289.822 \; \mathrm%7BkNm%7D $$
Rn Image Removed	Mathinline body --uriencoded--$$ \normalsize R_n = 0.6 F_u A_n = 0.6 \times 360 \times 9120 = 1969.92\; \mathrm%7BkN%7D $$
ΦRn Image Removed	Mathinline body --uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 1969.92 = 1477.44\; \mathrm%7BkN%7D $$

Bolt Shear at Support

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 body --uriencoded--$$ \normalsize A_b = \dfrac%7B \pi d%5e2%7D %7B4%7D = \dfrac%7B \pi 24%5e2%7D %7B4%7D = 452.389\; \mathrm%7Bmm%5e2%7D $$
Fnv Image Removed	Mathinline body --uriencoded--$$ \normalsize F_n = 0.450 F_%7Bub%7D = 0.450 \times 1000 =450\; \mathrm%7BN/mm%5e2%7D $$
Rn Image Removed	Mathinline body --uriencoded--$$ \normalsize R_n = F_n A_b = 4 \times 450 \times 452.389 \times 10%5e%7B-3%7D = 814.3\; \mathrm%7BkN%7D $$	AISC 360-16 J3-1
ΦRn Image Removed	Mathinline body --uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 814.3 = 610.725 \; \; \mathrm%7BkN%7D $$

Bolt Bearing on End Plate

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
Lc,edge Image Removed	Mathinline body --uriencoded--$$ \normalsize L_%7Bc,edge%7D = L_e - 0.5d_h = 51.519 - 0.5 \times 27 = 38.019\; \mathrm%7Bmm%7D $$
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(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
Lc,spacing Image Removed	Mathinline body --uriencoded--$$ \normalsize L_%7Bc,spacing%7D =157.767 - 27 = 130.767\; \mathrm%7Bmm%7D $$
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(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
Rn	Mathinline body --uriencoded--$$ \normalsize R_%7Bn%7D = n_eR_%7Bn,edge%7D + n_sR_%7Bn,spacing%7D $$ Mathinline body --uriencoded--$$ \normalsize R_%7Bn%7D = 2 \times 492.72 + 2 \times 622.08 = 2229.6 \; \mathrm%7BkN%7D $$
ΦRn Image Removed	Mathinline body --uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 2229.6 = 1672.2\; \mathrm%7BkN%7D $$

Weld Size

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The required end weld sizeis checked according to AISC DG-4.

Fyp	235000 kN/m2	AISC DG-4-2 nd 2.1.7
tbw	9 mm
Fe	480000 kN/m2
w Image Removed	Mathinline body --uriencoded--$$ \normalsize w \geq \dfrac %7B \varphi 0.6 F_%7Byp%7D t_%7Bwb%7D%7D %7B2 \varphi_w 0.6 F_e 0.707%7D%7D =\dfrac %7B 1 \times 0.6 \times 235 \times 9%7D %7B2 \times 0.75 \times 0.6 \times 480\times 0.707%7D%7D = 3.97\; \mathrm%7Bmm%7D $$

Required	Available	Ratio	Control
3.97 mm	8.487 mm	0.468	√

Weld Strength

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The required end weld strength is checked according to AISC DG-4.

w	8.487 mm
FE	480 N/mm2
le	190.193 mm
Rn Image Removed	Mathinline body --uriencoded--$$ \normalsize R_n = 2 \times 0.6 \times 480 \times 10%5e%7B-3%7D \times 0.707 \times 8.487 \times 190.193 = 657.34\; \mathrm%7BkN%7D $$	AISC DG-4-2 nd 2.1.8
ΦRn Image Removed	Mathinline body --uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 657.34 = 493\; \mathrm%7BkN%7D $$

Required	Available	Ratio	Control
5.313 kN	492.981 kN	0.011	√

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Related Topics

• End Plate Connections per AISC 358-16 & AISC 360-16

• Bolted Flange Plate Connections per AISC 358-16 & AISC 360-16

• Welded Flange Plate Connection per AISC 360-16

• Welded Web Connection (WUF-W Moment Connection) per AISC 358-16 & AISC 360-16

• Splice Connection with per AISC 360-16