09-Strength of Gusset Plate (Steel Structural Design & Prof. Shehab Mourad)

1. 1 Prepared by Prof. Shehab Mourad – Department of Civil Eng. - KSU
Strength of Gusset Plate
1) Yielding on gross area
Ø Rn = 0.9 * Fy * Ag
Ag = Area of gusset plate
Fy = Yield Tensile Strength of guest
2) Fracture at net area
Anet is the smaller value of
i) Anet = Ag - (dh* tgusset*Nb)
ii) Anet = 0.85 * Ag
Ø Rn = 0.75 * Fu * Anet
Fu = Ultimate Tensile Strength of gusset
Ag = Area of gusset plate
dh = Diameter of hole
Nb = Number of bolt
3) Block shear in gusset plate
case 1 (for two rows of bolts) case 2
Fig Block shear failure on gusset plate bolted connection
Agt = Lt*tgusset
Ant = Lt*tgusset – (Nb1*dh* tgusset)
Agv = Lv* tguest
Anv = Lv* tgusset – (Nb2*dh* tgusset)
Where
Lv = 2*Lv1 (for given case 1)
Lv = Lv1 (for given case 2)
Agt = gross Area in tensile
Lt
Lv 1
Lt
Lv 1
PuPu
SS Le2Le1 1
Le1 S Le2S
1
Gusset Plate
Nb1 = Number of bolt along Lt (for given case 1, Nb1= 1)
(for given case 2, Nb1= 3/2)
Nb2= Number of bolt along Lv (for given case 1, Nb2= 5)
(for given case 2, Nb2= 5/2)
If 0.6*Fu*Anv > Fu*Ant , Ø Rn = 0.75*(0.6*Fu*Anv + Fy*Agt)
If 0.6*Fu*Anv < Fu*Ant, Ø Rn = 0.75*(Fu*Ant + 0.6*Fy*Agv)

2. 2 Prepared by Prof. Shehab Mourad – Department of Civil Eng. - KSU
Example 3
Determine the factor tensile resistance of the given gusset plate
Fu = 400 MPa
Fy = 250 MPa
Gusset plate 165 X 12 mm
2L 89 x 76 x 6.4 mm
Le = 51 mm
s = 76 mm
dbolt = 19 mm
dhole = 19 + 3 = 22 mm
Fig Dimensions of bolted connection for gusset plate
Yielding on gross area
Ø Rn = 0.9 * Fy * Ag
= 0.9 * 250 * (165*12) / 1000 = 445.5 kN
Fracture at net area
Anet is the smaller value of
i) Anet =Ag - (dh* tgusset) = 165*12 – 22*12 = 1716 mm2
ii) Anet = 0.85*Ag = 0.85*165*12 = 1683 mm2
Anet = 1683 mm2
Ø Rn = 0.75 * Fu * Anet
= 0.75 * 400 * 1683 / 1000 = 504.9 kN
Block shear rupture.
Block shear failure on gusset
plate
∴ The factor tensile resistance of the gusset plate is Ø Rn = 445.5 kN
Lt = 76 mm
Lv = 203
Pu
Pu
SS Le2Le1 1
Le1 S Le2S
1
38 mm
38 mm
Agt = Lt * tguest = 76 * 12 = 912 mm2
Ant = Lt * tguest – (Nb1 * dh * tgusset) = 912 – 1/2 * (22*12) = 780 mm2
Agv = Lv * tguest = 203 * 12 = 2436 mm2
Anv = Lv * tguest – (Nb2 * dh * tgusset) = 2436 – 2.5* (22*12) = 1776 mm2
0.6 * Fu * Anv = 0.6 * 400 * 1776 / 1000 = 426.24 kN
Fu * Ant = 400 * 780 / 1000 = 312 kN
0.6 * Fu * Anv > Fu * Ant
Ø Rn = 0.75 * (0.6 * Fu * Anv + Fy * Agt)
= 0.75 * (426.24 + 250 * 912 / 1000) = 490.68 kN

3. 3 Prepared by Prof. Shehab Mourad – Department of Civil Eng. - KSU
Summary of result of strength of bolted tension memeber
Fu = 400 MPa
Fy = 250 MPa
Guest plate 165 X 12 mm
2L 89 x 76 x 6.4 mm
Le = 51 mm
s = 76 mm
dbolt = 19 mm
dhole = 19 + 3 = 22 mm
Strength of member.
Yielding of Ag = 459 kN
Fracture on Ae = 393.9 kN
Block share rupture = 432.2 kN
Strength of bolt
Slip- critical connection = 416.9 kN
Shear failure of bolt = 510 kN
Bearing failure of plate = 492.5 kN
Strength of gusset plate.
Yielding of Ag = 445.5 kN
Fracture on Ae = 504.9 kN
Block share rupture = 490.68 kN
The governing design strength of the bolted tension member = 393.9 kN
That is governed by fracture at effective area of the angles
Pu
Pu
SS Le2Le1 1
Le1 S Le2S
1
38 mm
38 mm