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How does ideCAD design Four Bolts Unstiffened End Plate Connection according to AISC 360358-16 & AISC 358360-16?

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Tip
Four bolts unstiffened 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	70 mm	L_eh ≥ 2d = 2 * 30 = 60 mm conformity check for application	√
L_e-min	38 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	85 mm	L _eh ≥ 2d = 2*30 = 60 mm conformity check for application	√
L_e-min	38 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
w	8.487 mm		√
w_min	5 mm	AISC 360-16 Table J2.4	√

Continuity Plate to Column Flange Weld Size

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

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

Continuity Plate to Column Web Weld Size

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

w ≥ w_min
w	11.315 mm		√
w_min	6 mm	AISC 360-16 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 ≤57
End plate width, b_p	290 mm	178≤ b_p ≤ 273
Horizontal distance between bolts, g	150 mm	102≤g≤152
p_fi	60 mm	38≤p_fi ≤114
p_fo	60 mm	38≤p_fo ≤114
Beam depth, d_b	450 mm	349≤ d_b ≤ 1400
Beam flange thickness, t_bf	15 mm	10≤t_bf ≤19
Beam flange width, b_bf	190	152≤b_bf ≤235
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 unstiffened end plate connection is checked according to AISC 358-16 §6.8

M_uc

796.489 kNm

AISC 358-16 (6.8-3)

F_t

750000 kN750 N/mmm²

h_o

Mathinline

body	--uriencoded--$$ \normalsize h_%7Bo%7D = d - \dfrac%7Bt_%7Bfo%7D%7D %7B2%7D + p_%7Bfo%7D = 450 - \dfrac %7B15%7D %7B2%7D + 60 = 502.5 \; \; \mathrm%7Bmm%7D $$

h₁

Mathinline

body	--uriencoded--$$ \normalsize h_%7B1%7D = d - 1.5t_%7Bfo%7D - p_%7Bfi%7D = 450 - 1.5 \times 15 - 60 = 367.5 \; \; \mathrm%7Bmm%7D $$

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--$$ \normalsize d_b \geq \sqrt%7B \dfrac %7B 2 \times 796.489%7D 489 \times 10%5e6%7D %7B0.90 \times \pi \times 750000 750 \times (502.5 + 367.5)%7D %7D =29.385 \; \; \mathrm%7Bmm%7D $$

Required	Available	Ratio	Control
29.385 mm	30 mm	0.979	√

End Plate Thickness

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

M_uc

796.489 kNm

AISC 358-16 (6.8-5)

F_yp

275000 kN275 N/mmm²

s

Mathinline

body	--uriencoded--$$ \normalsize s = \dfrac%7B1%7D%7B2%7D \sqrt%7B b_pg%7D = \dfrac%7B1%7D%7B2%7D \sqrt%7B 290 \times 150%7D = 104.28 $$

Y_p

Mathinline

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

Y_p

Mathinline

body	--uriencoded--$$ \small Y_p = \dfrac%7B290%7D%7B2%7D \left [ 367.5 \left ( \dfrac%7B1%7D%7B60%7D + \dfrac%7B1%7D%7B104.28%7D \right ) + 502.5 \left ( \dfrac%7B1%7D%7B60%7D \right ) - \dfrac%7B1%7D%7B2%7D \right ] + \dfrac%7B2%7D%7B150%7D [ 367.5(60 + 104.28 ) ] $$

Mathinline

body	--uriencoded--$$ \small Y_p = 3345.972\; \mathrm%7Bmm%7D $$

t_p

Mathinline

body	--uriencoded--$$ \normalsize t_p \geq \sqrt%7B \dfrac %7B 1.11 M_%7Buc%7D%7D %7B\varphi F_%7Byp%7DY_p%7D %7D = \sqrt%7B \dfrac %7B 1.11 \times 796.489%7D 489 \times 10%5e6 %7D %7B 1 \times 275000 275 \times 3345.972%7D %7D = 30.997 \; \; \mathrm%7Bmm%7D $$

Required	Available	Ratio	Control
30.997 mm	32 mm	0.969	√

End Plate Shear Yield

The shear yielding of the end plate is checked according to AISC 358-16 §6.8.

M_uc

796.489 kNm

AISC 358-16 (6.8-7)

F_f

Mathinline

body	--uriencoded--$$ \normalsize F_f = \dfrac %7BM_%7Buc%7D%7D%7Bd - t_f%7D = \dfrac %7B796.489%7D%7B450 - 15%7D 489%7D%7B(450 - 15) \times 10%5e%7B-3%7D %7D =1831.009 \; \mathrm%7BkN%7D $$

R_req = F_f / 2

Mathinline

body	--uriencoded--$$ \normalsize R_%7Breq%7D = \dfrac %7BF_f%7D%7B2%7D = \dfrac %7B1831.009%7D%7B2%7D =915.504 \; \mathrm%7BkN%7D $$

F_yp

275000 kN275 N/mmm²

b_p

290 mm

t_p

32 mm

d

450 mm

t_bf

15 mm

R_n

Mathinline

body	--uriencoded--$$ \normalsize R_n = 0.6F_%7Byp%7Db_pt_p $$

Mathinline

body	--uriencoded--$$ \normalsize R_n = 0.6 \times 275000 275 \times 290 \times 32 \times 10%5e%7B-3%7D = 1531.2 \; \; \mathrm%7BkN%7D $$

Required	Available	Ratio	Control
915.504 kN	1531.2 kN	0.598	√

End Plate Shear Rupture

The shear rupture of the end plate is checked according to AISC 358-16 §6.8.

M_uc

915796.504 489 kNm

AISC 358-16 (6.8-7)

F_f

Mathinline

body	--uriencoded--$$ \normalsize F_f = \dfrac %7BM_%7Buc%7D%7D%7Bd - t_f%7D = \dfrac %7B796.489%7D%7B450 - 15%7D 489%7D%7B(450 - 15) \times 10%5e%7B-3%7D%7D =1831.009 \; \mathrm%7BkN%7D $$

R _req = F_f / 2

Mathinline

body	--uriencoded--$$ \normalsize R_%7Breq%7D = \dfrac %7BF_f%7D%7B2%7D = \dfrac %7B1831.009%7D%7B2%7D =915.504\; \mathrm%7BkN%7D $$

F_up

410000 kN410 N/mmm²

A_n

Mathinline

body	--uriencoded--$$ \normalsize A_%7Bn%7D = 32 \times \dfrac %7B290%7D%7B2%7D =4640 $$\; \mathrm%7Bmm%5e2%7D$$

d

450 mm

t_bf

15 mm

R_n

Mathinline

body	--uriencoded--$$ \normalsize R_n = 0.6F_%7Bup%7DA_n = 0.6 \times 410000 410 \times 4640 \times 10%5e%7B-3%7D = 1141.44 \; \mathrm%7BkN%7D $$

ΦR_n

Mathinline

body	--uriencoded--$$ \normalsize \varphi R_n = 0.9 \times 1141.44 = 1027.3 \; \; \mathrm%7BkN%7D $$

Required	Available	Ratio	Control
915.504 kN	1027.3 kN	0.891	√

Bolt Shear Check

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

A_b

Mathinline

body	--uriencoded--$$ \normalsize A_%7Bb%7D = \dfrac %7B \pi d%5e2%7D%7B4%7D = \dfrac %7B \pi 30%5e2%7D%7B4%7D =706.858 \; \mathrm%7Bmm%5e2%7D $$

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--$$ \normalsize R_n = F_%7Bn%7DA_b = 4 \times 450 \times 706.858 \times 10%5e%7B-3%7D = 1272.34 \; \; \mathrm%7BkN%7D $$

ΦR_n

Mathinline

body	--uriencoded--$$ \normalsize \varphi R_n = 0.90 \times 1272.34 = 1145.11 \; \; \mathrm%7BkN%7D $$

Required	Available	Ratio	Control
270.986 kN	1145.11 kN	0.237	√

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

30+3=33 mm

L_c,edge

Mathinline

body	--uriencoded--$$ \normalsize L_%7Bc,edge%7D = L_e - 0.5d_h = 85 - 0.5 \times 33 = 68.5 \; \mathrm%7Bmm%7D $$

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(68.5)(32)(410 \times 10%5e%7B-3%7D) \\2.4(30)(32)(410 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D =944.64\; \mathrm%7BkN%7D

L_c,spacing

Mathinline

body	--uriencoded--$$ \normalsize L_%7Bc,spacing%7D = s - d_h = 150 - 1.5 \times 30 = 102 $$\; \mathrm%7Bmm%7D$$

R_n-spacing

Mathinline

body	--uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2(102)(32)(410 \times 10%5e%7B-3%7D) \\2.4(30)(32)(410 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D =944.64\; \mathrm%7BkN%7D

R_n

Mathinline

body	--uriencoded--$$ \normalsize R_n = n_e R_%7Bn-edge%7D + n_s R_%7Bn-spacing%7D = 4 \times 944.64 = 3778.56 \; \; \mathrm%7BkN%7D $$

ΦR_n

Mathinline

body	--uriencoded--$$ \normalsize \varphi R_n = 0.9 \times 3778.56 = 3400.704 \; \; \mathrm%7BkN%7D $$

Required	Available	Ratio	Control
270.986 kN	3400.704 kN	0.08	√

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_h

30+3=33 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--$$ \normalsize R_n = [ 2.4 (30) (31) (410 \times 10%5e%7B-3%7D ) ] = 915.12\; \mathrm%7BkN%7D $$

L_c,spacing

Mathinline

body	--uriencoded--$$ \normalsize L_%7Bc,spacing%7D = s - d_h = 150 - 1.5 \times 30 = 102 $$\; \mathrm%7Bmm%7D$$

R_n-spacing

Mathinline

body	--uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2(102)(32)(410 \times 10%5e%7B-3%7D) \\2.4(30)(31)(410 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D = 915.12\; \mathrm%7BkN%7D

R_n

Mathinline

body	--uriencoded--$$ \normalsize R_n = n_e R_%7Bn-edge%7D + n_s R_%7Bn-spacing%7D = 4 \times 915.12 = 3660.48 \; \; \mathrm%7BkN%7D $$

ΦR_n

Mathinline

body	--uriencoded--$$ \normalsize \varphi R_n = 0.9 \times 3660.48 = 3294.432 \; \; \mathrm%7BkN%7D $$

Required	Available	Ratio	Control
270.986 kN	3294.432 kN	0.082	√

Beam Web to End Plate Weld Size

The required end weld sizefor four bolts unstiffened 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--$$ \normalsize w \geq \dfrac %7B \varphi_t F_%7Byb%7D t_%7Bbw%7D%7D %7B2 \times \varphi \times 0.6 \times F_e \times 1.5 \times0.707%7D%7D $$

Mathinline

body	--uriencoded--$$ \normalsize = \dfrac %7B 0.9 \times 275 275000 \times 10%5e%7B-3%7D \times 9%7D %7B2 \times 0.75 \times 0.6 \times 490 490000 \times 10%5e%7B-3%7D \times 1.5 \times 0.707%7D%7D = 4.763 $$

Required	Available	Ratio	Control
4.763 mm	8.487 mm	0.561	√

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

796.489 kNm

AISC 358-16 (6.8-13)

F_yp

275000 kN275 N/mmm²

s

Mathinline

body	--uriencoded--$$ \normalsize s = \dfrac%7B1%7D%7B2%7D \sqrt%7B b_f g%7D = \dfrac%7B1%7D%7B2%7D \sqrt%7B 300 \times 150%7D = 106.066 066 \; \mathrm%7Bmm%7D $$

c

Mathinline

body	--uriencoded--$$ \normalsize c = p_%7Bfo%7D + t_%7Bfo%7D + p_%7Bfi%7D = 60 + 16 + 60 = 136\; \mathrm%7Bmm%7D $$

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--$$ \tiny small Y_c = \dfrac%7B300%7D%7B2%7D \left [ 367.5 \left ( \dfrac%7B1%7D%7B106.066%7D \right ) + 502.5 \left ( \dfrac%7B1%7D%7B106.066%7D \right ) \right ] $$

Mathinline

body	--uriencoded--$$ \small + \dfrac%7B2%7D%7B150%7D \left [ 367.5 \left ( 106.066 + \dfrac%7B3 \times 136 %7D%7B4%7D \right ) + 502.5 \left ( 106.066 + \dfrac%7B136%7D%7B4%7D \right ) + \dfrac%7B136%5e2%7D%7B2%7D \right ] + \dfrac%7B150%7D%7B2%7D $$

Mathinline

body	--uriencoded--$$ \normalsize Y_c = 5344.209\; \mathrm%7Bmm%7D $$

t_cf

Mathinline

body	--uriencoded--$$ \normalsize t_%7Bcf%7D \geq \sqrt%7B \dfrac %7B 1.11 M_%7Buc%7D%7D %7Buc%7D %7D %7B\varphi F_%7Byc%7DY_c%7D %7D = \sqrt%7B \dfrac %7B 1.11 \times 796.489%7D %7B 1 489 \times 275 10%5e%7B6%7D%7D %7B1 \times 10%5e%7B-3%7D 275\times 5344.209%7D %7D %7D = 24.527 \; \mathrm%7Bmm%7D $$

Required	Available	Ratio	Control
24.527 mm	31 mm	0.791	√

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

P_r

366.473 kN

AISC 360-16 J10-9

P_y

Mathinline

body	--uriencoded--\normalsize P_%7By%7D = F_y A_g = 275 \times 10%5e%7B-3%7D \times 28634.759 = 7874.559 \; \; \mathrm%7BkN%7D

F_y

275000 kN275 N/mmm²

A _g

28634.759 mm²

d_c

650 mm

t_w

16 mm

R_n

Mathinline

body	--uriencoded--$$ \normalsize R_n = 0.6F_%7By%7Dd_ct_w = 0.6 \times 275 \times 10%5e%7B-3%7D \times 650 \times 16 = 1716 \; \; \mathrm%7BkN%7D $$

ΦR_n

Mathinline

body	--uriencoded--$$ \normalsize \varphi R_n = 1 \times 1716 = 1716 \; \; \mathrm%7BkN%7D $$

Required	Available	Ratio	Control
1621.957 kN	1716 kN	0.945	√

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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Required	Available	Ratio	Control
11.2 mm	16 mm	0.700	√

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Next Topic

4 Bolts Unstiffened End Plate Connection Report 1

Related Topics

Versions Compared

Old Version 20

New Version Current

Key

Connection Geometry

GEOMETRY CHECKS

Horizontal Edge Distance

Vertical Edge Distance

Beam web 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 Shear Yield

End Plate Shear Rupture

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