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How does ideCAD design four bolts stiffened end plate connection according to AISC 360358-16 & AISC 358360-16?

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Tip
Four bolts stiffened end plate connection is designed automatically according to the AISC 358-16 and AISC 360-16 by the ideCAD Structural.

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A_b: Non-threaded bolt web characteristic cross-sectional area
A_g: Gross area
A_n: Net cross-section area
A_e: Effective net cross-sectional area
A_vg: Gross area under shear stress
A_nv: Net area under shear stress
A_nt: Net area under tensile stress
A_w: Cross-section web area
b_bf = width of beam flange, in. (mm)
b_p = width of end-plate, in. (mm)
d = depth of connecting beam, in. (mm)
g = horizontal distance between bolts, in. (mm)
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
n_sp: Number of slip planes
s: Distance between bolt-holecenters
L: Connector distance
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
p_b = vertical distance between the inner and outer row of bolts in an eight-bolt stiffened connection, in. (mm)
p_fi = vertical distance from the inside of a beam tension flange to the nearest inside bolt row, in. (mm)
p_fo = vertical distance from the outside of a beam tension flange to the nearest outside bolt row, in. (mm)
t_bf = thickness of beam flange, in. (mm)
t_p = thickness of end-plate, in. (mm)
R_n: Characteristic strength
R_nt: Characteristic tensile strength
R_nv: Characteristic shear strength

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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.

L_eh ≥ L _e-min	AISC 360-16 J3.4
L_eh	72 mm	L_eh ≥ 2d = 2 * 30 = 60 mm conformity check for application	√
L_e-min	46 mm	Minimum distance check according to Table J3.4	√

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.

L_ev ≥ L _e-min	AISC 360-16 J3.4
L_ev	72 mm	L_ev ≥ 2d = 2 * 30 = 60 mm conformity check for application	√
L_e-min	46 mm	Minimum distance check according to Table J3.4	√

Beam Web to End Plate Weld Size

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

w ≥ w_min	AISC 360-16
w	7.072 mm		√
w_min	5 mm	Table J2.4	√

Stiffener to Beam Flange Weld Size

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

w ≥ w_min	AISC 360-16
w	7.072 mm		√
w_min	5 mm	Table J2.4	√

Stiffener to End Plate Weld Size

The minimum size welds are checked according to AISC 360-16 Table J2.4

w ≥ w_min	AISC 360-16
w	7.072 mm		√
w_min	5 mm	Table J2.4	√

Continuity Plate to Column Flange Weld Size

The minimum size welds are checked according to AISC 360-16 Table J2.4

w ≥ w_min	AISC 360-16
w	11.315 mm		√
w_min	6 mm	Table J2.4	√

Continuity Plate to Column Web Weld Size

The minimum size welds are checked according to AISC 360-16 Table J2.4

w ≥ w_min	AISC 360-16
w	11.315 mm		√
w_min	6 mm	Table J2.4	√

Prequalification Limits (AISC 358-16 Table 6.1)

All end-plate moment connection configurations should satisfy these beam and column limitations. Beam and column limitations are given in AISC 358-16 Table 6.1.

Beam span / Beam cross-section height	9144 mm /450 mm=20.32	≥7.0
End plate thickness, t_p	32 mm	13≤t_p ≤38
End plate width, b_p	290 mm	178≤ b_p ≤ 273
Horizontal distance between bolts, g	150 mm	83≤g≤152
p_fi	60 mm	44≤p_fi ≤140
p_fo	60 mm	44≤p_fo ≤140
Beam depth, d_b	450 mm	349≤d_b≤610
Beam flange thickness, t_bf	15 mm	10≤t_bf ≤19
Beam flange width, b_bf	190	152≤b_bf ≤229
Column depth	650	≤ 920 mm
Bolt grade	10.9	8.8 - 10.9
Min yield stress of the end plate material	275 MPa	235 /275 / 355 MPa
Flange plate weld	CJP	CJP

STRENGTH CHECKS

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Bolt diameter

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

M_uc

821.813 kNm

AISC 358-16 (6.8-3)

F_t

750000 kN/m²

h_o

Mathinline

body	--uriencoded--$$ \normalsize h_o = d - \frac %7Bt_%7Bfo%7D%7D%7B2%7D + p_%7Bfo%7D = 450 - \frac %7B15%7D%7B2%7D + 72 = 514.5\; \mathrm%7Bmm%7D $$

h₁

Mathinline

body	--uriencoded--$$ \normalsize h_1 = d - 1.5 t_%7Bfo%7D - p_%7Bfi%7D = 450 - 1.5 \times 15 -72 = 355.5\; \mathrm%7Bmm%7D $$

d_b

Mathinline

body	--uriencoded--$$ \normalsize d_b \geq \sqrt%7B \dfrac %7B 2 M_%7Buc%7D%7D %7B\varphi \pi F_t(h_o + h_1)%7D %7D $$

Mathinline

body	--uriencoded--$$ \normalsize d_b \geq \sqrt%7B \dfrac %7B 2 \times 821.813%7D 813 \times 10%5e6%7D %7B0.90 \times \pi \times 750000 750 \times (514.5 + 355.5)%7D %7D =29.825 \; \; \mathrm%7Bmm%7D $$

Required	Available	Ratio	Control
29.825 mm	36 mm	0.829	√

End Plate Thickness

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

M_uc

821.813kNm

AISC 358-16 (6.8-5)

F_yp

275000 kN/m²

s

Mathinline

body	--uriencoded--$$ \normalsize s = \dfrac%7B1%7D%7B2%7D \sqrt%7B b_p g%7D = \dfrac%7B1%7D%7B2%7D \sqrt%7B 298 \times 154%7D = 107.112\; \mathrm%7Bmm%7D $$

Y_p

Mathinline

body	--uriencoded--$$ \small Y_p = \dfrac%7Bb_p%7D%7B2%7D \left [ h_1 \left ( \dfrac%7B1%7D%7Bp_%7Bfi%7D%7D + \dfrac%7B1%7D%7Bs%7D \right ) + h_0 \left ( \dfrac%7B1%7D%7Bp_%7Bfo%7D%7D + \dfrac%7B1%7D%7B2s%7D \right ) \right ] + \dfrac%7B2%7D%7Bg%7D \left [ h_1 \left ( p_%7Bfi%7D +s \right ) + h_o \left ( d_%7Be%7D + p_%7Bfo%7D \right ) \right ] $$

Y_p

Mathinline

body	--uriencoded--$$ \normalsize Y_p = \dfrac%7B298%7D%7B2%7D \left [ 355.5 \left ( \dfrac%7B1%7D%7B72%7D + \dfrac%7B1%7D%7B107.112%7D \right ) + 514.5 \left ( \dfrac%7B1%7D%7B72%7D + \dfrac%7B1%7D%7B2 \times 107.112 %7D \right ) \right ] $$

Mathinline

body	--uriencoded--$$ \normalsize + \dfrac%7B2%7D%7B154%7D \left [ 355.5 \left ( 72 + 107.112 \right ) + 514.5 \left ( 72 + 72 \right ) \right ] =4441.914 \; \mathrm%7Bmm%7D $$

t_p

Mathinline

body	--uriencoded--$$ \normalsize t_p \geq \sqrt%7B \dfrac %7B 1.11 M_%7Buc%7D%7D %7B\varphi F_%7Byc%7DY_p%7D %7D = \sqrt%7B \dfrac %7B 1.11 \times 821.813%7D 813\times 10%5e%7B6%7D%7D %7B 1 \times 275 \times 10%5e%7B-3%7D \times 4441.914%7D %7D = 27.327 \; \mathrm%7Bmm%7D $$

Required	Available	Ratio	Control
27.327 mm	30 mm	0.911	√

End Plate Stiffener Thickness

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

t_bw

9 mm

AISC 358-16 (6.8-9)

F_yb

275000 kN/m²

F_ys

275000 kN/m²

t_s

12 mm

Mathinline

body	--uriencoded--$$ \normalsize t_s \geq t_%7Bbw%7D \dfrac %7B F_%7Byb%7D%7D %7BF_%7Bys%7D%7D $$

Mathinline

body	--uriencoded--$$ \normalsize 12 \; \mathrm%7Bmm%7D \geq 9 \times \dfrac %7B 275000%7D %7B275000%7D =9 \; \mathrm%7Bmm%7D $$

Required	Available	Ratio	Control
9 mm	12 mm	0.750	√

End Plate Stiffener Local Buckling

Stiffener local buckling limit statefor four bolts stiffened end plate connection is checked according to AISC 358-16 §6.8

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Required	Available	Ratio	Control
12	15.102	0.795	√

Stiffener to Beam Flange Weld Size

The required end weld sizefor four bolts stiffened end plate connection is checked.

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Required	Available	Ratio	Control
6.35	7.072	0.898	√

Stiffener to End Plate Weld Size

The required end weld sizefor four bolts stiffened end plate connection is checked.

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Required	Available	Ratio	Control
6.35	7.072	0.898	√

Bolt Shear Check

The shear limit state of end plate bolts is checked according to AISC 360-16.

A_b

Mathinline

body	--uriencoded--$$ \normalsize A_%7Bb%7D = \dfrac %7B \pi d%5e2%7D%7B4%7D = \dfrac %7B \pi 36%5e2%7D%7B4%7D =1017.876 \; \mathrm%7Bmm%5e2%7D $$

AISC 358-16 6.8.11

F_n

Mathinline

body	--uriencoded--$$ \normalsize F_n = 0.450F_%7Bub%7D = 0.450 \times 1000 = 450 \; \mathrm%7BN/mm%5e2%7D $$

R_n

Mathinline

body	--uriencoded--$$ \normalsize R_n = F_%7Bn%7DA_b = 4 \times 450 \times 1017.876 \times 10%5e%7B-3%7D = 1832.177 \; \; \mathrm%7BkN%7D $$

ΦR_n

Mathinline

body	--uriencoded--$$ \normalsize \varphi R_n = 0.9 \times 1832.177 = 1648.959 \; \; \mathrm%7BkN%7D $$

Required	Available	Ratio	Control
271.371 kN	1648.959 kN	0.165	√

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.

d_h

36+3=39 mm

L_c,edge

Mathinline

body	--uriencoded--$$ \normalsize L_%7Bc,edge%7D = L_e - 0.5d_h = 72 - 0.5 \times 39 = 52.5 $$\; \mathrm%7Bmm%7D$$

R_n

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 358-16 6.8-12

R_n-edge

Mathinline

body	--uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2(52.5)(30)(410000 410 \times 10%5e%7B-3%7D) \\2.4(36)(30)(410000 410 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D =774.9 \; \; \mathrm%7BkN%7D

L_c,spacing

Mathinline

body	--uriencoded--$$ \normalsize L_%7Bc,spacing%7D = 72 + 72 + 15 - 39 = 120 \; \mathrm%7Bmm%7D $$

R_n-spacing

Mathinline

body	--uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2(120)(30)(410000 410 \times 10%5e%7B-3%7D) \\2.4(36)(30)(410000 410 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D =1062.72\; \mathrm%7BkN%7D

R_n

Mathinline

body	--uriencoded--$$ \normalsize R_n = n_e R_%7Bn-edge%7D + n_s R_%7Bn-spacing%7D $$

Mathinline

body	--uriencoded--$$ \normalsize R_n = 2 \times 774.9 + 2 \times 1062.72 = 3675.24 \; \; \mathrm%7BkN%7D $$

ΦR_n

Mathinline

body	--uriencoded--$$ \normalsize \varphi R_n = 0.9 \times 3675.24 = 3307.716 \; \; \mathrm%7BkN%7D $$

Required	Available	Ratio	Control
271.371 kN	3307.716 kN	0.082	√

Bolt Bearing on Column Flange

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.

d_b

36 mm

R_n

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 358-16 6.8-12

R_n-edge

Mathinline

body	--uriencoded--$$ \normalsize R_n = [ 2.4 (36) (31) (410000 410 \times 10%5e%7B-3%7D ) ] = 1098.144\; \mathrm%7BkN%7D $$

L_c,spacing

Mathinline

body	--uriencoded--$$ \normalsize L_%7Bc,spacing%7D = 72+ 72 +15 - 39 = 120 $$\; \mathrm%7Bmm%7D$$

R_n-spacing

Mathinline

body	--uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2(120)(31)(410000 410 \times 10%5e%7B-3%7D) \\2.4(36)(31)(410000 410 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D = 1098.144\; \mathrm%7BkN%7D

R_n

Mathinline

body	--uriencoded--$$ \normalsize R_n = n_e R_%7Bn-edge%7D + n_s R_%7Bn-spacing%7D $$

Mathinline

body	--uriencoded--$$ \normalsize R_n = 2 \times 1098.144 + 2 \times 1098.144 = 4392.576 \; \; \mathrm%7BkN%7D $$

ΦR_n

Mathinline

body	--uriencoded--$$ \normalsize \varphi R_n = 0.9 \times 4392.576 = 3953.318 \; \; \mathrm%7BkN%7D $$

Required	Available	Ratio	Control
271.371 kN	3953.318 kN	0.069	√

Beam Web to End Plate Weld Size

The required end weld sizefor four bolts stiffened end plate connection is checked according to AISC 358-16 §6.7

F_yp

275000 kN/m²

AISC 358-16

(6.7.6) 3

t_bw

9 mm

F _e

490000 kN/m²

w

Mathinline

body	--uriencoded--$$ \normalsize w \geq \dfrac %7B \varphi_t F_%7Byb%7D t_%7Bbw%7D%7D %7B2 \times \varphi \times 0.6 F_e \times 1.5 \times 0.707%7D%7D $$

Mathinline

body	--uriencoded--$$ \normalsize = \dfrac %7B 0.9 \times 275 \times 10%5e%7B-3%7D \times 9%7D %7B2 \times 0.75 \times 0.6 \times 490 \times 10%5e%7B-3%7D \times 1.5 \times 0.707%7D%7D = 4.763 \; \; \mathrm%7Bmm%7D $$

Required	Available	Ratio	Control
4.763 mm	7.072 mm	0.673	√

Column Flange Thickness

The required column flange thickness, t_cf,for four bolts unstiffened end plate connection is checked according to AISC 358-16 §6.8

M_uc

821.813 kNm

AISC 358-16 (6.8-13)

F_yp

275000 kN275 N/mmm²

s

Mathinline

body	--uriencoded--$$ \normalsize s = \dfrac%7B1%7D%7B2%7D \sqrt%7B b_f g%7D = \dfrac%7B1%7D%7B2%7D \sqrt%7B 300 \times 154%7D = 107.471\; \mathrm%7Bmm%7D $$

c

Mathinline

body	--uriencoded--$$ \normalsize c = p_%7Bfo%7D + t_%7Bfo%7D + p_%7Bfi%7D = 72 + 16 + 72 = 160\; \mathrm%7Bmm%7D $$

Y_c

Mathinline

body	--uriencoded--$$ \small Y_c = \dfrac%7Bb_f%7D%7B2%7D \left [ h_1 \left ( \dfrac%7B1%7D%7Bs%7D \right ) + h_0 \left ( \dfrac%7B1%7D%7Bs%7D \right ) \right ] + \dfrac%7B2%7D%7Bg%7D \left [ h_1 \left ( s + \dfrac%7B3c%7D%7B4%7D \right ) + h_0 \left ( s + \dfrac%7Bc%7D%7B4%7D \right ) + \dfrac%7Bc%5e2%7D%7B2%7D \right ] + \dfrac%7Bg%7D%7B2%7D $$

Y_c

Mathinline

body	--uriencoded--$$ \normalsize Y_c = \dfrac%7B300%7D%7B2%7D \left [ 355.5 \left ( \dfrac%7B1%7D%7B107.471%7D \right ) + 514.5 \left ( \dfrac%7B1%7D%7B107.471%7D \right ) \right ] $$

Mathinline

body	--uriencoded--$$ \normalsize + \dfrac%7B2%7D%7B154%7D \left [ 355.5 \left ( 107.471 + \dfrac%7B3 \times 160 %7D%7B4%7D \right ) + 514.5 \left ( 107.471 + \dfrac%7B160%7D%7B4%7D \right ) $$

Mathinline

body	--uriencoded--$$ \normalsize + \dfrac%7B160%5e2%7D%7B2%7D \right ] + \dfrac%7B154%7D%7B2%7D =5054.57 \; \mathrm%7Bmm%7D $$

t_cf

Mathinline

body	--uriencoded--$$ \normalsize t_%7Bcf%7D \geq \sqrt%7B \dfrac %7B 1.11 M_%7Buc%7D%7D %7B\varphi F_%7Byc%7DY_c%7D %7D = \sqrt%7B \dfrac %7B 1.11 \times 821.813%7D 813 \times 10%5e%7B6%7D %7D %7B 1 \times 275 \times 10%5e%7B-3%7D \times 5054.57%7D %7D = 25.618\; \mathrm%7Bmm%7D $$

Required	Available	Ratio	Control
25.618 mm	31 mm	0.826	√

Column Panel Zone Shear

Yielding of the column panel zonefor four bolts unstiffened end plate connection is checked according to AISC 360-16 §J.10

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Required	Available	Ratio	Control
1673.526 kN	1716 kN	0.975	√

Panel Zone Thickness

The required panel zone thickness for four bolts unstiffened end plate connection is checked according to AISC 358-16.

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Related Topics

Versions Compared

Old Version 16

New Version Current

Key

Connection Geometry

GEOMETRY CHECKS

Horizontal Edge Distance

Vertical Edge Distance

Beam Web to End Plate Weld Size

Stiffener to Beam Flange Weld Size

Stiffener to End Plate Weld Size

Continuity Plate to Column Flange Weld Size

Continuity Plate to Column Web Weld Size

Prequalification Limits (AISC 358-16 Table 6.1)

STRENGTH CHECKS

Bolt diameter

End Plate Thickness

End Plate Stiffener Thickness

End Plate Stiffener Local Buckling

Stiffener to Beam Flange Weld Size

Stiffener to End Plate Weld Size

Bolt Shear Check

Bolt Bearing on End Plate

Bolt Bearing on Column Flange

Beam Web to End Plate Weld Size

Column Flange Thickness

Column Panel Zone Shear

Panel Zone Thickness