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Lecture Notes #28 Design of Gusset plate

Professor Guowei Ma Office: 160 Tel: 61-8-6488-3102 Email: [email protected]

1

Gusset Plate • Flat structural elements used to connect adjacent members meeting at truss panel joints and at diagonal brace connections. • Help transmit loads from one member to another. • Maybe welded or bolted to the members meeting at the joints. • Minimum thickness used in design practice is usually 10 mm.

2

Gusset Plate at a Diagonal Brace

3

Gusset Plate at a Truss Panel Point

4

Gusset Plate at a Truss Panel Point

5

Gusset Plate at a Truss Panel Point

6

Gusset Plate at a Truss Support

7

Design of Gusset Plate • For diagonal bracing connection, several connection interfaces must be designed: diagonal brace-to-gusset connection gusset-to-column connection beam-to-column connection • At truss joints, the gusset plates connect the web members to the chord members • The centroidal axes of the members meeting at the joint coincide at one point, called the work point (WP) 8

Design of Gusset Plate • Moment may be induced in the gusset plate and the adjoining members if it is not feasible to have a common WP • Shear and axial stresses • Whitmore effective width, lw Projecting lines at an angle of spread of 30˚ on both side of the connection starting from the first row of bolts to the last row of bolts For welded connections, projected on both sides of the longitudinal weld to the end of the weld

9

Design of Gusset Plate • Effective gross area Whitmore effective width, lw times the plate thickness, t • End of the bracing member or truss web member terminates at least a distance of 2t away from the reentrant corner of the gusset plate at the gusset-to-column interfaces • Above requirement can be relaxed for connections subject to monotonic or static loading

10

Out-of-Plane Buckling • Unbraced length, Lg the larger of the length of the plate between adjacent lines of bolts parallel to the direction of the axial compression force, or the length of the plate along the centroidal axis of the diagonal brace or truss web member between the end of the brace or truss web member and the connected edge of the gusset plate. • Buckling is assumed to occur over a plate width equal to the Whitmore effective width, lw 11

Out-of-Plane Buckling φN c = φσ cr lwt l w:

Whitmore effective width

t:

Thickness of the gusset plate

Φ:

0.9

σcr:

The critical buckling stress

12

Buckling of the Free or Unsupported Edge

13

Buckling of the Free or Unsupported Edge • Gusset plate under monotonic or static loading

t ≥ 0.5 L fg

fy E

• Gusset plate subject to cyclic (or seismic) loading

t ≥ 1.33L fg

fy E

14

Yielding of Gusset Plate • Design tension or compression yield strength

φN s = φf y lwt Tension yielding is the most desirable form of failure because of the ductility associated with this failure mode

15

Tension Failure Tension failure of the gusset plate due to fracture at a bolt line within the Whitmore effective area

φN s = φf u (lw − nd hole )t f u : Tensile strength of the gusset plate φ : 0.75 n : Number of bolt holes perpendicular to the applied axial force for each line d hole : Diameter of bolt hole Least desirable form of failure because of the sudden and brittle nature of this failure mode 16

Combined Actions 2

2

N V M + ≤ 1.0 + φM s φN s φVs *

*

*

17

Example For the truss joint shown below, the gusset plate is made of Grade 400 steel with a yield stress fy= 400 MPa, and tensile strength fu=520 MPa assuming a M20 bolts of Property Class 4.6, determine i) Whitmore effective width for the gusset plate on diagonal web members A and B ii) Compression buckling capacity of the gusset plate on diagonal member A iii) Tension capacity of the gusset plate on diagonal member B 18

16 mm thick 376 kN

Gusset plate

271 kN 271 kN

19

40

75 mm

20

Solution 1)

lwA = 40 + bA + LwA tan θ = 40 + 80 + 150 tan 30° = 206.6 mm lwB = bB + 2 LwB tan θ = 80 + 2 ×150 tan 30° = 253.2 mm

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2)

Lg = 75 mm 1 1 3 I A = lwAt = (206.6)(16) 3 = 70519.5 mm 4 12 12 206.6 mm

rA =

Lg

75 = = 16.2 rA 4.62 π 2 EI 3.14 2 (200 ×109 )(70519.5 ×10 −12 ) N cr = 2 = le (75 ×10 −3 ) 2

75 mm

IA 70519.5 = = 4.62 mm A (206.6)(16)

= 2.4721×107 N = 24721 kN

φN c = φN cr = 0.9 × 24721 = 22249 kN 22

3)

Tension yielding capacity of the gusset plate on the diagonal element B

φN t = φf y Ag = (0.9)(400 ×106 ) × (16 ×10 −3 )(253.2 ×103 ) = 1458.4 kN Tension capacity of the gusset plate due fracture

φN t = φ 0.85 f u Au = (0.9)(0.85)(520 × 106 ) × (16 ×10 −3 )(253.2 − 2 × 22) ×10 −3 = 1331.5 kN

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Professor Guowei Ma Office: 160 Tel: 61-8-6488-3102 Email: [email protected]

1

Gusset Plate • Flat structural elements used to connect adjacent members meeting at truss panel joints and at diagonal brace connections. • Help transmit loads from one member to another. • Maybe welded or bolted to the members meeting at the joints. • Minimum thickness used in design practice is usually 10 mm.

2

Gusset Plate at a Diagonal Brace

3

Gusset Plate at a Truss Panel Point

4

Gusset Plate at a Truss Panel Point

5

Gusset Plate at a Truss Panel Point

6

Gusset Plate at a Truss Support

7

Design of Gusset Plate • For diagonal bracing connection, several connection interfaces must be designed: diagonal brace-to-gusset connection gusset-to-column connection beam-to-column connection • At truss joints, the gusset plates connect the web members to the chord members • The centroidal axes of the members meeting at the joint coincide at one point, called the work point (WP) 8

Design of Gusset Plate • Moment may be induced in the gusset plate and the adjoining members if it is not feasible to have a common WP • Shear and axial stresses • Whitmore effective width, lw Projecting lines at an angle of spread of 30˚ on both side of the connection starting from the first row of bolts to the last row of bolts For welded connections, projected on both sides of the longitudinal weld to the end of the weld

9

Design of Gusset Plate • Effective gross area Whitmore effective width, lw times the plate thickness, t • End of the bracing member or truss web member terminates at least a distance of 2t away from the reentrant corner of the gusset plate at the gusset-to-column interfaces • Above requirement can be relaxed for connections subject to monotonic or static loading

10

Out-of-Plane Buckling • Unbraced length, Lg the larger of the length of the plate between adjacent lines of bolts parallel to the direction of the axial compression force, or the length of the plate along the centroidal axis of the diagonal brace or truss web member between the end of the brace or truss web member and the connected edge of the gusset plate. • Buckling is assumed to occur over a plate width equal to the Whitmore effective width, lw 11

Out-of-Plane Buckling φN c = φσ cr lwt l w:

Whitmore effective width

t:

Thickness of the gusset plate

Φ:

0.9

σcr:

The critical buckling stress

12

Buckling of the Free or Unsupported Edge

13

Buckling of the Free or Unsupported Edge • Gusset plate under monotonic or static loading

t ≥ 0.5 L fg

fy E

• Gusset plate subject to cyclic (or seismic) loading

t ≥ 1.33L fg

fy E

14

Yielding of Gusset Plate • Design tension or compression yield strength

φN s = φf y lwt Tension yielding is the most desirable form of failure because of the ductility associated with this failure mode

15

Tension Failure Tension failure of the gusset plate due to fracture at a bolt line within the Whitmore effective area

φN s = φf u (lw − nd hole )t f u : Tensile strength of the gusset plate φ : 0.75 n : Number of bolt holes perpendicular to the applied axial force for each line d hole : Diameter of bolt hole Least desirable form of failure because of the sudden and brittle nature of this failure mode 16

Combined Actions 2

2

N V M + ≤ 1.0 + φM s φN s φVs *

*

*

17

Example For the truss joint shown below, the gusset plate is made of Grade 400 steel with a yield stress fy= 400 MPa, and tensile strength fu=520 MPa assuming a M20 bolts of Property Class 4.6, determine i) Whitmore effective width for the gusset plate on diagonal web members A and B ii) Compression buckling capacity of the gusset plate on diagonal member A iii) Tension capacity of the gusset plate on diagonal member B 18

16 mm thick 376 kN

Gusset plate

271 kN 271 kN

19

40

75 mm

20

Solution 1)

lwA = 40 + bA + LwA tan θ = 40 + 80 + 150 tan 30° = 206.6 mm lwB = bB + 2 LwB tan θ = 80 + 2 ×150 tan 30° = 253.2 mm

21

2)

Lg = 75 mm 1 1 3 I A = lwAt = (206.6)(16) 3 = 70519.5 mm 4 12 12 206.6 mm

rA =

Lg

75 = = 16.2 rA 4.62 π 2 EI 3.14 2 (200 ×109 )(70519.5 ×10 −12 ) N cr = 2 = le (75 ×10 −3 ) 2

75 mm

IA 70519.5 = = 4.62 mm A (206.6)(16)

= 2.4721×107 N = 24721 kN

φN c = φN cr = 0.9 × 24721 = 22249 kN 22

3)

Tension yielding capacity of the gusset plate on the diagonal element B

φN t = φf y Ag = (0.9)(400 ×106 ) × (16 ×10 −3 )(253.2 ×103 ) = 1458.4 kN Tension capacity of the gusset plate due fracture

φN t = φ 0.85 f u Au = (0.9)(0.85)(520 × 106 ) × (16 ×10 −3 )(253.2 − 2 × 22) ×10 −3 = 1331.5 kN

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