How does ideCAD design Four Bolts Unstiffened End Plate Connection according to AISC 360358-16 & AISC 358360-16?
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Ab: Non-threaded bolt web characteristic cross-sectional area
Ag: Gross area
An: Net cross-section area
Ae: Effective net cross-sectional area
Avg: Gross area under shear stress
Anv: Net area under shear stress
Ant: Net area under tensile stress
Aw: Cross-section web area
bbf = width of beam flange, in. (mm)
bp = width of end-plate, in. (mm)
d = depth of connecting beam, in. (mm)
g = horizontal distance between bolts, in. (mm)
dh: Bolt hole diameter
Fy: Structural steel characteristic yield strength
Fu: Structural steel characteristic tensile strength
Fyb: Bolt characteristic yield strength
Fub: Bolt characteristic tensile strength
nsp: Number of slip planes
s: Distance between bolt-holecenters
L: Connector distance
Lc: The clear distance between bolt holes
Le: The distance from the center of the bolt hole to the edge of the assembled element
Leh: The horizontal distance from the center of the bolt hole to the edge of the assembled element
Lev: The vertical distance from the center of the bolt hole to the edge of the assembled element
pb = vertical distance between the inner and outer row of bolts in an eight-bolt stiffened connection, in. (mm)
pfi = vertical distance from the inside of a beam tension flange to the nearest inside bolt row, in. (mm)
pfo = vertical distance from the outside of a beam tension flange to the nearest outside bolt row, in. (mm)
tbf = thickness of beam flange, in. (mm)
tp = thickness of end-plate, in. (mm)
Rn: Characteristic strength
Rnt: Characteristic tensile strength
Rnv: 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.
Leh ≥ Le-min | AISC 360-16 J3.4 | | |
Leh | 70 mm | Leh ≥ 2d = 2 * 30 = 60 mm conformity check for application | √ |
Le-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.
Lev ≥ Le-min | AISC 360-16 J3.4 | | |
Lev | 85 mm | L eh ≥ 2d = 2*30 = 60 mm conformity check for application | √ |
Le-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 ≥ wmin | | | |
w | 8.487 mm | | √ |
wmin | 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 ≥ wmin | | | |
w | 11.315 mm | | √ |
wmin | 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 ≥ wmin | | | |
w | 11.315 mm | | √ |
wmin | 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, tp | 32 mm | 13≤tp ≤57 |
End plate width, bp | 290 mm | 178≤ bp ≤ 273 |
Horizontal distance between bolts, g | 150 mm | 102≤g≤152 |
pfi | 60 mm | 38≤pfi ≤114 |
pfo | 60 mm | 38≤pfo ≤114 |
Beam depth, db | 450 mm | 349≤ db ≤ 1400 |
Beam flange thickness, tbf | 15 mm | 10≤tbf ≤19 |
Beam flange width, bbf | 190 | 152≤bbf ≤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, db, for four bolts unstiffened end plate connection is checked according to AISC 358-16 §6.8
Muc | 796.489 kNm | AISC 358-16 (6.8-3) |
Ft | 750000 kN750 N/mmm2 | |
ho | | Mathinline |
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| body | --uriencoded--$$ \normalsize h_%7Bo%7D = d - \dfrac%7Bt_%7Bfo%7D%7D %7B2%7D + p_%7Bfo%7D = 450 - \dfrac %7B15%7D %7B2%7D + 60 = 502.5 \; \; \mathrm%7Bmm%7D $$ |
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h1 | | Mathinline |
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| body | --uriencoded--$$ \normalsize h_%7B1%7D = d - 1.5t_%7Bfo%7D - p_%7Bfi%7D = 450 - 1.5 \times 15 - 60 = 367.5 \; \; \mathrm%7Bmm%7D $$ |
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db | | Mathinline |
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| body | --uriencoded--$$ \normalsize d_b \geq \sqrt%7B \dfrac %7B 2 M_%7Buc%7D%7D %7B\varphi \pi F_t(h_o + h_1)%7D %7D $$ |
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| body | --uriencoded--$$ \normalsize d_b \geq \sqrt%7B \dfrac %7B 2 \times 796.489%7D 489 \times 10%5e6%7D %7B0.90 \times \pi \times 750000 750 \times (502.5 + 367.5)%7D %7D =29.385 \; \; \mathrm%7Bmm%7D $$ |
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Required | Available | Ratio | Control |
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29.385 mm | 30 mm | 0.979 | √ |
End Plate Thickness
The required end plate thickness, tb, for four bolts unstiffened end plate connection is checked according to AISC 358-16 §6.8
Muc | 796.489 kNm | AISC 358-16 (6.8-5) |
Fyp | 275000 kN275 N/mmm2 | |
s | | Mathinline |
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| body | --uriencoded--$$ \normalsize s = \dfrac%7B1%7D%7B2%7D \sqrt%7B b_pg%7D = \dfrac%7B1%7D%7B2%7D \sqrt%7B 290 \times 150%7D = 104.28 $$ |
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Yp | | Mathinline |
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| body | --uriencoded--$$ \normalsize Y_p = \dfrac%7Bb_p%7D%7B2%7D \left [ h_1 \left ( \dfrac%7B1%7D%7Bp_%7Bfi%7D%7D + \dfrac%7B1%7D%7Bs%7D \right ) + h_0 \left ( \dfrac%7B1%7D%7Bp_%7Bfo%7D%7D \right ) - \dfrac%7B1%7D%7B2%7D \right ] + \dfrac%7B2%7D%7Bg%7D [ h_1 (p_%7Bfi%7D + s ) ] $$ |
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Yp | | Mathinline |
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| body | --uriencoded--$$ \small Y_p = \dfrac%7B290%7D%7B2%7D \left [ 367.5 \left ( \dfrac%7B1%7D%7B60%7D + \dfrac%7B1%7D%7B104.28%7D \right ) + 502.5 \left ( \dfrac%7B1%7D%7B60%7D \right ) - \dfrac%7B1%7D%7B2%7D \right ] + \dfrac%7B2%7D%7B150%7D [ 367.5(60 + 104.28 ) ] $$ |
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| body | --uriencoded--$$ \small Y_p = 3345.972\; \mathrm%7Bmm%7D $$ |
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tp | | Mathinline |
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| body | --uriencoded--$$ \normalsize t_p \geq \sqrt%7B \dfrac %7B 1.11 M_%7Buc%7D%7D %7B\varphi F_%7Byp%7DY_p%7D %7D = \sqrt%7B \dfrac %7B 1.11 \times 796.489%7D 489 \times 10%5e6 %7D %7B 1 \times 275000 275 \times 3345.972%7D %7D = 30.997 \; \; \mathrm%7Bmm%7D $$ |
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Required | Available | Ratio | Control |
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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.
Muc | 796.489 kNm | AISC 358-16 (6.8-7) |
Ff | | Mathinline |
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| body | --uriencoded--$$ \normalsize F_f = \dfrac %7BM_%7Buc%7D%7D%7Bd - t_f%7D = \dfrac %7B796.489%7D%7B450 - 15%7D 489%7D%7B(450 - 15) \times 10%5e%7B-3%7D %7D =1831.009 \; \mathrm%7BkN%7D $$ |
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Rreq = Ff / 2 | | Mathinline |
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| body | --uriencoded--$$ \normalsize R_%7Breq%7D = \dfrac %7BF_f%7D%7B2%7D = \dfrac %7B1831.009%7D%7B2%7D =915.504 $$\; \mathrm%7BkN%7D $$ |
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Fyp | 275000 kN275 N/mmm2 | |
bp | 290 mm | |
tp | 32 mm | |
d | 450 mm | |
tbf | 15 mm | |
Rn | | Mathinline |
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| body | --uriencoded--$$ \normalsize R_n = 0.6F_%7Byp%7Db_pt_p $$ |
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| body | --uriencoded--$$ \normalsize R_n = 0.6 \times 275000 275 \times 290 \times 32 \times 10%5e%7B-3%7D = 1531.2 \; \; \mathrm%7BkN%7D $$ |
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Required | Available | Ratio | Control |
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915.504 kN | 1531.2 kN | 0.598 | √ |
End Plate Shear Rupture
The shear rupture of the end plate is checked according to AISC 358-16 §6.8.
Muc | 915796.504 489 kNm | AISC 358-16 (6.8-7) |
Ff | | Mathinline |
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| body | --uriencoded--$$ \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 $$ |
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R req = Ff / 2 | | Mathinline |
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| body | --uriencoded--$$ \normalsize R_%7Breq%7D = \dfrac %7BF_f%7D%7B2%7D = \dfrac %7B1831.009%7D%7B2%7D =915.504\; \mathrm%7BkN%7D $$ |
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Fup | 410000 kN410 N/mmm2 | |
An | | Mathinline |
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| body | --uriencoded--$$ \normalsize A_%7Bn%7D = 32 \times \dfrac %7B290%7D%7B2%7D =4640 $$\; \mathrm%7Bmm%5e2%7D$$ |
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d | 450 mm | |
tbf | 15 mm | |
Rn | | Mathinline |
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| body | --uriencoded--$$ \normalsize R_n = 0.6F_%7Bup%7DA_n = 0.6 \times 410000 410 \times 4640 \times 10%5e%7B-3%7D = 1141.44 \; \mathrm%7BkN%7D $$ |
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ΦRn | | Mathinline |
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| body | --uriencoded--$$ \normalsize \varphi R_n = 0.9 \times 1141.44 = 1027.3 \; \; \mathrm%7BkN%7D $$ |
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Required | Available | Ratio | Control |
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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.
Ab | | Mathinline |
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| body | --uriencoded--$$ \normalsize A_%7Bb%7D = \dfrac %7B \pi d%5e2%7D%7B4%7D = \dfrac %7B \pi 30%5e2%7D%7B4%7D =706.858 \; \mathrm%7Bmm%5e2%7D $$ |
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Fn | | Mathinline |
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| body | --uriencoded--$$ \normalsize F_n = 0.450F_%7Bub%7D = 0.450 \times 1000 = 450 \; \mathrm%7BN/mm%5e2%7D $$ |
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Rn | | Mathinline |
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| body | --uriencoded--$$ \normalsize R_n = F_%7Bn%7DA_b = 4 \times 450 \times 706.858 \times 10%5e%7B-3%7D = 1272.34 \; \; \mathrm%7BkN%7D $$ |
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ΦRn | | Mathinline |
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| body | --uriencoded--$$ \normalsize \varphi R_n = 0.90 \times 1272.34 = 1145.11 \; \; \mathrm%7BkN%7D $$ |
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Required | Available | Ratio | Control |
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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.
dh | 30+3=33 mm | |
Lc,edge | | Mathinline |
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| body | --uriencoded--$$ \normalsize L_%7Bc,edge%7D = L_e - 0.5d_h = 85 - 0.5 \times 33 = 68.5 \; \mathrm%7Bmm%7D $$ |
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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 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 358-16 6.8-12 |
Rn-edge | | Mathinline |
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| 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 |
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Lc,spacing | | Mathinline |
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| body | --uriencoded--$$ \normalsize L_%7Bc,spacing%7D = s - d_h = 150 - 1.5 \times 30 = 102 $$\; \mathrm%7Bmm%7D$$ |
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Rn-spacing | | Mathinline |
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| body | --uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2(102)(32)(410 \times 10%5e%7B-3%7D) \\2.4(30)(32)(410 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D =944.64\; \mathrm%7BkN%7D |
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Rn | | Mathinline |
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| body | --uriencoded--$$ \normalsize R_n = n_e R_%7Bn-edge%7D + n_s R_%7Bn-spacing%7D = 4 \times 944.64 = 3778.56 \; \; \mathrm%7BkN%7D $$ |
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ΦRn | | Mathinline |
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| body | --uriencoded--$$ \normalsize \varphi R_n = 0.9 \times 3778.56 = 3400.704 \; \; \mathrm%7BkN%7D $$ |
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Required | Available | Ratio | Control |
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270.986 kN | 3400.704 kN | 0.08 | √ |
Bolt Bearing on Column Flange
Bearing strength limit states of the connection plate that are “shear tear out” and “ovalization of bolt hole” for both end and inner bolts are checked according to AISC 360-16.
dh | 30+3=33 mm | |
Rn | | Mathinline |
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| body | --uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2L_c \times t \times F_u \\2.4d \times t \times F_u \end%7Bmatrix%7D\right] \end%7Baligned%7D |
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| AISC 358-16 6.8-12 |
Rn-edge | | Mathinline |
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| body | --uriencoded--$$ \normalsize R_n = [ 2.4 (30) (31) (410 \times 10%5e%7B-3%7D ) ] = 915.12\; \mathrm%7BkN%7D $$ |
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Lc,spacing | | Mathinline |
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| body | --uriencoded--$$ \normalsize L_%7Bc,spacing%7D = s - d_h = 150 - 1.5 \times 30 = 102 $$\; \mathrm%7Bmm%7D$$ |
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Rn-spacing | | Mathinline |
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| 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 |
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Rn | | Mathinline |
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| body | --uriencoded--$$ \normalsize R_n = n_e R_%7Bn-edge%7D + n_s R_%7Bn-spacing%7D = 4 \times 915.12 = 3660.48 \; \; \mathrm%7BkN%7D $$ |
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ΦRn | | Mathinline |
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| body | --uriencoded--$$ \normalsize \varphi R_n = 0.9 \times 3660.48 = 3294.432 \; \; \mathrm%7BkN%7D $$ |
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Required | Available | Ratio | Control |
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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
Muc | 796.489 kNm | AISC 358-16 (6.8-13) |
Fyp | 275000 kN/m2 | |
s |  Image Removed | |
c |  Image Removed | |
Yc |  Image Removed | |
Yc |  Image Removed | |
tcf |  Image Removed | |
Fyp | 275000 kN/m2 | AISC 358-16 6.7.6 (3) |
tbw | 9 mm | |
Fe | 490000 kN/m2 | |
w  Image Removed | | |
Required | Available | Ratio | Control |
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4.763 mm | 8.487 mm | 0.561 | √ |
Column Flange Thickness
The required column flange thickness, tcf, for four bolts unstiffened end plate connection is checked according to AISC 358-16 §6.8
| body | --uriencoded--$$ \normalsize w \geq \dfrac %7B \varphi_t F_%7Byb%7D t_%7Bbw%7D%7D %7B2 \times \varphi \times 0.6 \times F_e \times 1.5 \times0.707%7D%7D $$ |
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| body | --uriencoded--$$ \normalsize = \dfrac %7B 0.9 \times 275000 \times 10%5e%7B-3%7D \times 9%7D %7B2 \times 0.75 \times 0.6 \times 490000 \times 10%5e%7B-3%7D \times 1.5 \times 0.707%7D%7D = 4.763 $$ |
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Required | Available | Ratio | Control |
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4.763 mm | 8.487 mm | 0.561 | √ |
Column Flange Thickness
The required column flange thickness, tcf, for four bolts unstiffened end plate connection is checked according to AISC 358-16 §6.8
Muc | 796.489 kNm | AISC 358-16 (6.8-13) |
Fyp | 275 N/mm2 | |
s | | Mathinline |
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| body | --uriencoded--$$ \normalsize s = \dfrac%7B1%7D%7B2%7D \sqrt%7B b_f g%7D = \dfrac%7B1%7D%7B2%7D \sqrt%7B 300 \times 150%7D = 106.066 \; \mathrm%7Bmm%7D $$ |
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c | | Mathinline |
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| body | --uriencoded--$$ \normalsize c = p_%7Bfo%7D + t_%7Bfo%7D + p_%7Bfi%7D = 60 + 16 + 60 = 136\; \mathrm%7Bmm%7D $$ |
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Yc | | Mathinline |
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| body | --uriencoded--$$ \small Y_c = \dfrac%7Bb_f%7D%7B2%7D \left [ h_1 \left ( \dfrac%7B1%7D%7Bs%7D \right ) + h_0 \left ( \dfrac%7B1%7D%7Bs%7D \right ) \right ] + \dfrac%7B2%7D%7Bg%7D \left [ h_1 \left ( s + \dfrac%7B3c%7D%7B4%7D \right ) + h_0 \left ( s + \dfrac%7Bc%7D%7B4%7D \right ) + \dfrac%7Bc%5e2%7D%7B2%7D \right ] + \dfrac%7Bg%7D%7B2%7D $$ |
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Yc | | Mathinline |
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| body | --uriencoded--$$ \small Y_c = \dfrac%7B300%7D%7B2%7D \left [ 367.5 \left ( \dfrac%7B1%7D%7B106.066%7D \right ) + 502.5 \left ( \dfrac%7B1%7D%7B106.066%7D \right ) \right ] $$ |
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| body | --uriencoded--$$ \small + \dfrac%7B2%7D%7B150%7D \left [ 367.5 \left ( 106.066 + \dfrac%7B3 \times 136 %7D%7B4%7D \right ) + 502.5 \left ( 106.066 + \dfrac%7B136%7D%7B4%7D \right ) + \dfrac%7B136%5e2%7D%7B2%7D \right ] + \dfrac%7B150%7D%7B2%7D $$ |
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| Mathinline |
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| body | --uriencoded--$$ \normalsize Y_c = 5344.209\; \mathrm%7Bmm%7D $$ |
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tcf | | Mathinline |
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| body | --uriencoded--$$ \normalsize t_%7Bcf%7D \geq \sqrt%7B \dfrac %7B 1.11 M_%7Buc%7D %7D %7B\varphi F_%7Byc%7DY_c%7D %7D = \sqrt%7B \dfrac %7B 1.11 \times 796.489 \times 10%5e%7B6%7D%7D %7B1 \times 275\times 5344.209%7D %7D %7D = 24.527 \; \mathrm%7Bmm%7D $$ |
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Required | Available | Ratio | Control |
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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
Pr | 366.473 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 \times 28634.759 = 7874.559 \; \; \mathrm%7BkN%7D |
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Fy | 275000 kN275 N/mmm2 | |
A g | 28634.759 mm2 | |
d c | 650 mm | |
tw | 16 mm | |
Rn |  Image Removed | |
ΦRn |  Image Removed | .759 mm2 | |
d c | 650 mm | |
tw | 16 mm | |
Rn | | Mathinline |
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| body | --uriencoded--$$ \normalsize R_n = 0.6F_%7By%7Dd_ct_w = 0.6 \times 275 \times 10%5e%7B-3%7D \times 650 \times 16 = 1716 \; \; \mathrm%7BkN%7D $$ |
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ΦRn | | Mathinline |
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| body | --uriencoded--$$ \normalsize \varphi R_n = 1 \times 1716 = 1716 \; \; \mathrm%7BkN%7D $$ |
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Required | Available | Ratio | Control |
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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.
tmin ≥u/180  Image Removed | | Mathinline |
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| body | --uriencoded--$$ \normalsize t_%7Bmin%7D = 16 \geq 2016/180 = 11.2 \; \; \mathrm%7Bmm%7D $$ |
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tmin = t w | 16 mm | |
tw | 16 mm | |
u | 2016 mm | |
Required | Available | Ratio | Control |
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11.2 mm | 16 mm | 0.700 | √ |
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