Bracing connection, gusset plate design. Brace line B1

PROJECT: STEEL BUILDING DESIGN CASE STUDY
SUBJECT: Bracing connection, gusset plate design.
Brace line B1, second floor.
φ = resistance factor
Fy = specified (ASTM) minimum yield stress
Fu = specified (ASTM) minimum tensile strength
Rn = strength
t = thickness of connected part
Pu = factored load to be resisted
d = diameter of the bolt
eb = one-half the depth of the beam, in.
ec = one-half the depth of the column, in.
db = depth of the beam, in.
dc = depth of the column, in.
w.p. = working point.
N = horizontal distance of gusset plate, in.
V = vertical distance of gusset plate, in.
α = distance from the face of the column flange to the centroid of the gusset-to-beam connection, in.
β = distance from the face of the beam flange to the centroid of the gusset-to-column connection, in.
Aw =cross section area of the whitmore section
Elevation View
Plan View
Member A-E, Interior floor girder:
W24x68 ASTM 992
db = 23.7 in
Fy = 50 ksi
Fu = 65 ksi
Member A-B, Interior column:
W10x49 ASTM 992
dc = 9.98 in
Fy = 50 ksi
Fu = 65 ksi
Member A-C, Brace:
2L6x4x1/2LLBB A36
Fy = 36 ksi
Fu = 58 ksi
13
Pu = 127.0 k
B C D 96 k
A E
30
W.P.
Column
W10x49
Gusset Plate
Brace
2L6x4x1/2
SHEET 122 of 131
Girder
W24x68
13
15
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PROJECT: STEEL BUILDING DESIGN CASE STUDY
SUBJECT: Bracing connection, gusset plate design.
Use A325-N bolts in standard holes,3/4 in diameter.
Design shear strength of one bolt, double shear (LRFD Table 7-10)
Check bearing strength @ each bolt hole:
φRn = φ (2.4 * d * t * Fu) =
(φ = 0.75)
Check tension yielding on the Whitmore section:
y
Column
Brace
30°
kips > 31.8 kips
Gusset Plate Whitmore section
6
Girder
SHEET 123 of 131
φRn = 31.8 k
y = tan 30 o * 6 = in
*Note: Assume simplified Whitmore section (double
dashed area) for the purpose of this lab. This design will
be more conservative.
φRn = φ (Fu * Aw) =
(φ = 0.9)
kips > kips
Aw = (y + y + 2.5(Perp. distance between center of holes))*0.5
15
13
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PROJECT: STEEL BUILDING DESIGN CASE STUDY
SUBJECT: Bracing connection, gusset plate design.
Distribution of brace force to beam and column:
(Uniform force method)
From the member and frame geometry
eb = db/2 = in θ
ec = dc/2 = in 13
tanθ =
15
in order to remain free of moments on the connection interfaces, the following expression must be satisfied:
tan θ * eb - ec = α - β * tan θ
α - β * tan θ =
V
Try a gusset plate :
in
allow 1/2 in. between gusset and column
for the setback
in. x in. horizontally x
in. vertically
α = in
β = in
α' = tan θ * eb - ec + β * tan θ =
α − α' =
W.P.
β
ec
0.5
in
α
N
Column
Gusset Plate
Use α = in and β = in
N = in
V = in
in
Brace
eb
Girder
SHEET 124 of 131
15
13
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