Page Comparison

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How does ideCAD design brace-center connection according to AISC 360-16?

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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
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
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
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: Plate thickness
w = Size of weld leg, in. (mm)
R_n: Characteristic strength
U_bs: A coefficient considering the spread of tensile stresses

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Connection Geometry

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Brace-to-Gusset Plate Connection

GEOMETRY CHECKS

Bolt Spacing

The distance between the centers of bolts is checked per AISC 360-16.

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.

Weld Size

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

STRENGTH CHECKS

Bolt Shear at Brace

The bolt shear limit state of the connection is checked according to AISC 360-16.

Ab

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	Mathinline body --uriencoded--$$ \normalsize A_b = \dfrac%7B \pi d%5e2%7D %7B4%7D = \dfrac%7B \pi 20%5e2%7D %7B4%7D = 314.159\; \mathrm%7Bmm%5e2%7D $$
Fn

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R_n

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	Mathinline body --uriencoded--$$ \normalsize F_n = 0.450 F_%7Bub%7D = 0.450 \times 1000 =450 \; \mathrm%7BN/mm%5e2%7D $$
Rn	Mathinline body --uriencoded--$$ \normalsize R_n = F_n A_b = 2 \times 450 \times 314.159 \times 10%5e%7B-3%7D =282.743 \; \mathrm%7BkN%7D $$	AISC 360-16 J3-1
ΦRn

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Mathinline body --uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 282.743 = 212.058 \; \mathrm%7BkN%7D $$

Bolt Bearing on Plate

The bearing strength limit states of the connection plate, which are “shear tear out” and “ovalization of bolt hole” for both end and inner bolts, are checked according to AISC 360-16.

dh	20+2=22 mm
Lc,edge

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Mathinline body --uriencoded--$$ \normalsize L_%7Bc,edge%7D = L_e - 0.5d_h = 45 - 0.5 \times 22 =34 \; \mathrm%7Bmm%7D $$
Rn

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	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

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	Mathinline body --uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2(34)(15)(470 \times 10%5e%7B-3%7D) \\2.4(20)(15)(470 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D =287.64\; \mathrm%7BkN%7D
Lc,spacing

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	Mathinline body --uriencoded--$$ \normalsize L_%7Bc,spacing%7D = s - d_h = 60 - 22 =38\; \mathrm%7Bmm%7D $$
Rn-spacing

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R_n

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Mathinline body --uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2(38)(15)(470 \times 10%5e%7B-3%7D) \\2.4(20)(15)(470 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D =321.48\; \mathrm%7BkN%7D
Rn	Mathinline body --uriencoded--$$ \normalsize R_%7Bn%7D = n_eR_%7Bn,edge%7D + n_sR_%7Bn,spacing%7D $$ Mathinline body --uriencoded--$$ \normalsize R_%7Bn%7D = 1 \times 287.64 + 1 \times 321.48 = 609.12 \; \mathrm%7BkN%7D \; $$
ΦRn

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Mathinline body --uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 609.12 = 456.84 \; \mathrm%7BkN%7D $$

Bolt Bearing on Gusset

The bearing strength limit states of the connection plate, which are “shear tear out” and “ovalization of bolt hole” for both end and inner bolts, are checked according to AISC 360-16.

dh	20+2=22 mm
Lc,edge

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	Mathinline body --uriencoded--$$ \normalsize L_%7Bc,edge%7D = L_e - 0.5d_h = 45 - 0.5 \times 22 = 34 \; \mathrm%7Bmm%7D $$
Rn

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	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

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	Mathinline body --uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2(34)(10)(470 \times 10%5e%7B-3%7D) \\2.4(20)(10)(470 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D =191.76\; \mathrm%7BkN%7D
Lc,spacing

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	Mathinline body --uriencoded--$$ \normalsize L_%7Bc,spacing%7D = s - d_h = 60 - 22 =38 $$
Rn-spacing

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	Mathinline body --uriencoded--\begin%7Baligned%7D \normalsize R_n = \mathrm%7Bmin%7D \left[\begin%7Bmatrix%7D 1.2(38)(10)(470 \times 10%5e%7B-3%7D) \\2.4(20)(10)(470 \times 10%5e%7B-3%7D) \end%7Bmatrix%7D\right] \end%7Baligned%7D =214.32\; \mathrm%7BkN%7D
Rn

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	Mathinline body --uriencoded--$$ \normalsize R_%7Bn%7D = n_eR_%7Bn,edge%7D + n_sR_%7Bn,spacing%7D $$ Mathinline body --uriencoded--$$ \normalsize R_%7Bn%7D = 1 \times 191.76 + 1 \times 214.32 = 406.08 \; \mathrm%7BkN%7D $$
ΦRn

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Mathinline body --uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 406.08 = 304.56 \; \mathrm%7BkN%7D $$

Weld Strength

The nominal and design strength of the weld is checked according to AISC 360-16

Fe	490000 kN/m2
w	5.658 mm
Fu-plate	469.999  N/mm2
Fu-brace	410 N/mm2
tplate	15 mm	AISC 360-16 J3-6a
tbrace	15 mm
lw	150 mm
Rnw

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	Mathinline body --uriencoded--$$ \normalsize R_%7Bnw%7D = 0.6 \times F_%7Be%7D \times 2 \times 0.707 \times w $$ Mathinline body --uriencoded--$$ \normalsize R_%7Bnw%7D =0.6 \times 490 \times 2 \times 2 \times 0.707 \times 5.658 = 4704 \; \mathrm%7BkN/m%7D $$
Rn-plate

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R_nBM

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R_n

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ΦR_n

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	Mathinline body --uriencoded--$$ \normalsize R_%7Bn,plate%7D = 0.6 F_%7Bu%7D t l = 0.6 \times 2 \times469.999 \times 15 =8460 \; \mathrm%7BkN/m%7D $$
RnBM	Mathinline body --uriencoded--$$ \normalsize R_n = \mathrm%7Bmin%7D ( R_%7Bn,plate%7D , R_%7Bn,brace%7D ) =8460 \; \mathrm%7BkN/m%7D $$
Rn	Mathinline body --uriencoded--$$ \normalsize R_n = \mathrm%7Bmin%7D ( R_%7Bnw%7D , R_%7BnBM%7D )l =4704 \times 150 \times 10%5e%7B-3%7D =705.6\; \mathrm%7BkN%7D $$
ΦRn	Mathinline body --uriencoded--$$ \normalsize \varphi R_n = 0.75 \times 705.6 = 529.2 \; \mathrm%7BkN%7D $$

Whitmore Section Compression Yield

The buckling limit state in withmore section of the plate subjected to compression is checked according to AISC 360-16.

K	0.65
L	0 mm
r	2.887 mm
KL / r	0
Fy	355 N/mm2
Ag	1292.82 mm2
Rn

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	Mathinline body --uriencoded--$$ \normalsize R_n = F_y A_g = 355 \times 1292.82 \times 10%5e%7B-3%7D =458.95 \; \mathrm%7BkN%7D $$	AISC 360-16 J4-6
ΦRn

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Mathinline body --uriencoded--$$ \normalsize \varphi R_n = 0.90 \times 458.95 = 413.056 \; \mathrm%7BkN%7D $$

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