68402: Structural Design of Buildings II

1
68402 Structural Design of Buildings II
Design of Connections

• Monther Dwaikat
• Assistant Professor
• Department of Building Engineering
• An-Najah National University

2
Bolted Connections

• Types of Connections
• Simple Bolted Shear Connections
• Bearing and Slip Critical Connections
• Eccentric Bolted Connections
• Moment Resisting Bolted Connections
• Simple Welded Connections
• Eccentric Welded Connections
• Moment Resisting Welded Connections

3
Types of Connections
Simple Connections
Eccentric Connections
Bolted Connections
Welded Connections
Common Bolts
High Strength Bolts
Filet Weld
Slip Critical
Groove Weld
Bearing Type
4
Types of Connections
Simple Connections
Eccentric Connections
Bolted Connections
Welded Connections
Elastic Analysis
Ultimate Analysis
Moment Resisting
Elastic Analysis
Ultimate Analysis
Moment Resisting
5
Simple Bolted Connections

• There are different types of bolted connections.
  They can be categorized based on the type of
  loading.
• Tension member connection and splice. It subjects
  the bolts to forces that tend to shear the shank.
  
• Beam end simple connection. It subjects the bolts
  to forces that tend to shear the shank.
• Hanger connection. The hanger connection puts the
  bolts in tension

6
Simple Bolted Connections
P
P
Tension member Connection/ splice
P
P
Beam end Simple shear connection
7
Simple Bolted Connections
P
P
P
Hanger connection (Tension)
Moment resisting connection
8
Simple Bolted Connections

• The bolts are subjected to shear or tension
  loading.
• In most bolted connection, the bolts are
  subjected to shear.
• Bolts can fail in shear or in tension.
• You can calculate the shear strength or the
  tensile strength of a bolt
• Simple connection If the line of action of the
  force acting on the connection passes through the
  center of gravity of the connection, then each
  bolt can be assumed to resist an equal share of
  the load.
• The strength of the simple connection will be
  equal to the sum of the strengths of the
  individual bolts in the connection.

9
Bolt Types Materials

• A307 - Unfinished (Ordinary or Common) bolts
  low carbon steel A36, Fu 413 MPa,
• for light structures under static load
• A325 - High strength bolts, heat-treated medium
  carbon steel, Fu 827 MPa,
• for structural joints
• A490 - High strength bolts, Quenched and
  Tempered Alloy steel, Fu 1033 MPa
• for structural joints
• A449 - High strength bolts with diameter gt 1 ½,
  anchor bolts, lifting hooks, tie-downs

10
Common Bolts

• ASTM A307 bolts
• Common bolts are no longer common for current
  structural design but are still available

11
High Strength Bolts

• High strength bolts (HSB) are available as ASTM A
  325 and ASTM A490

Courtesy of Kao Wang Screw Co., Ltd.

• Advantages of HSB over A307 bolts
• Fewer bolts will be used compared to 307 è
  cheaper connection!
• Smaller workman force required compared to 307
• Higher fatigue strength
• Ease of bolt removal è changing connection

12
High Strength Bolts

• Snug tight
• All plies of the connection are in firm contact
  to each other No pretension is used.
• Easer to install and to inspect
• Pre-tensioned
• Bolts are first brought to snug tight status
• Bolts are then tensioned to 70 of their tensile
  stresses

Courtesy of www.halfpricesurplus.com

• Bolts are tensioned using direct tension
  indicator, calibrated wrench or other methods
  (see AISC)
• Slip critical
• Bolts are pre-tensioned but surfaces shall be
  treated to develop specific friction.
• The main difference is in design, not
  installation. Load must be limited not to exceed
  friction capacity of the connection (Strength Vs.
  Serviceability!)
• Necessary when no slip is needed to prevent
  failure due to fatigue in bridges.

13
HSB Bearing Type Connections

• The shear strength of bolts shall be determined
  as follows

AISC Table J3.2
The table bellow shows the values of fv (MPa) for
different types of bolts

• If the level of threads is not known, it is
  conservative to assume that the threads are type
  N.

14
Bolted Shear Connections

• We want to design the bolted shear connections so
  that the factored design strength (?Rn) is
  greater than or equal to the factored load. ? Rn
  ? Pu
• So, we need to examine the various possible
  failure modes and calculate the corresponding
  design strengths.
• Possible failure modes are
• Shear failure of the bolts
• Failure of member being connected due to fracture
  or yielding or .
• Edge tearing or fracture of the connected plate
• Tearing or fracture of the connected plate
  between two bolt holes
• Excessive bearing deformation at the bolt hole

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Failure Modes of Bolted Connections

• Bolt Shearing
• Tension Fracture
• Plate Bearing
• Block Shear

16
Actions on Bolt

• Shear, bearing, bending

Bearing and single plane Shear
Lap Joint
Bending
Bearing and double plane Shear
Butt Joint
17
Bolted Shear Connections

• Possible failure modes
• Failure of bolts single or double shear
• Failure of connected elements
• Shear, tension or bending failure of the
  connected elements (e.g. block shear)
• Bearing failure at bolt location

18
Bolted Shear Connections

• Shear failure of bolts
• Average shearing stress in the bolt fv P/A
  P/(?db2/4)
• P is the load acting on an individual bolt
• A is the area of the bolt and db is its diameter
• Strength of the bolt P fv x (?db2/4) where fv
  shear yield stress 0.6Fy
• Bolts can be in single shear or double shear as
  shown above.
• When the bolt is in double shear, two
  cross-sections are effective in resisting the
  load. The bolt in double shear will have the
  twice the shear strength of a bolt in single
  shear.

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Bolted Shear Connections
20
Bolted Shear Connections

• Failure of connected member
• We have covered this in detail in this course on
  tension members
• Member can fail due to tension fracture or
  yielding.
• Bearing failure of connected/connecting part due
  to bearing from bolt holes
• Hole is slightly larger than the fastener and the
  fastener is loosely placed in hole
• Contact between the fastener and the connected
  part over approximately half the circumference of
  the fastener
• As such the stress will be highest at the radial
  contact point (A). However, the average stress
  can be calculated as the applied force divided by
  the projected area of contact

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Bolted Shear Connections

• Average bearing stress fp P/(db t), where P is
  the force applied to the fastener.
• The bearing stress state can be complicated by
  the presence of nearby bolt or edge. The bolt
  spacing and edge distance will have an effect on
  the bearing strength.
• Bearing stress effects are independent of the
  bolt type because the bearing stress acts on the
  connected plate not the bolt.
• A possible failure mode resulting from excessive
  bearing close to the edge of the connected
  element is shear tear-out as shown below. This
  type of shear tear-out can also occur between two
  holes in the direction of the bearing load.
• Rn 2 x 0.6 Fu Lc t 1.2 Fu Lc t

22
Bolted Shear Connections

• The bearing strength is independent of the bolt
  material as it is failure in the connected metal
• The other possible common failure is shear end
  failure known as shear tear-out at the
  connection end

Shear limitation
Bearing limitation
23
Bolted Shear Connections
24
Bolted Shear Connections
25
Spacing and Edge-distance requirements

• The AISC code gives guidance for edge distance
  and spacing to avoid tear out shear

AISC Table J3.4
NOTE The actual hole diameter is 1.6 mm bigger
than the bolt, we use another 1.6 mm for
tolerance when we calculate net area. Here use
1.6 mm only not 3.2

• Bolt spacing is a function of the bolt diameter
• Common we assume
• The AISC minimum spacing is

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Bolt Spacings Edge Distances

• Bolt Spacings
• - Painted members or members not subject to
  corrosion
• 2 2/3d Bolt
  Spacings 24t or 305 mm
• (LRFD J3.3) (LRFD
  J3.5)
• - Unpainted members subject to corrosion
• 3d Bolt
  Spacings 14t or 178 mm
• Edge Distance
• Values in Table J3.4M Edge Distance 12t or
  152 mm
• (LRFD J3.4) (LRFD J3.5)
• d - bolt diameter
• t - thickness of thinner plate

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Bolted Shear Connections

• To prevent excessive deformation of the hole, an
  upper limit is placed on the bearing load. This
  upper limit is proportional to the fracture
  stress times the projected bearing area
• Rn C x Fu x bearing area C Fu db t
• If deformation is not a concern then C 3, If
  deformation is a concern then C 2.4
• C 2.4 corresponds to a deformation of 6.3 mm.
• Finally, the equation for the bearing strength of
  a single bolts is ?Rn
• where, ? 0.75 and Rn 1.2 Lc t Fu lt 2.4 db t
  Fu
• Lc is the clear distance in the load direction,
  from the edge of the bolt hole to the edge of the
  adjacent hole or to the edge of the material

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Bolted Shear Connections

• This relationship can be simplified as follows
• The upper limit will become effective when 1.2
  Lc t Fu gt 2.4 db t Fu
• i.e., the upper limit will become effective when
  Lc gt 2 db
• If Lc lt 2 db, Rn 1.2 Lc t Fu
• If Lc gt 2 db, Rn 2.4 db t Fu
• Fu - specified tensile strength of the connected
  material
• Lc - clear distance, in the direction of the
  force, between the edge of the hole and the edge
  of the adjacent hole or edge of the material.
• t - thickness of connected material

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Important Notes
Lc Clear distance
30
Design Provisions for Bolted Shear Connections

• In a simple connection, all bolts share the load
  equally.

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Design Provisions for Bolted Shear Connections

• In a bolted shear connection, the bolts are
  subjected to shear and the connecting/connected
  plates are subjected to bearing stresses.

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Design Provisions for Bolted Shear Connections

• The shear strength of all bolts shear strength
  of one bolt x number of bolts
• The bearing strength of the connecting /
  connected plates can be calculated using
  equations given by AISC specifications.
• The tension strength of the connecting /
  connected plates can be calculated as discussed
  in tension members.

33
AISC Design Provisions

• Chapter J of the AISC Specifications focuses on
  connections.
• Section J3 focuses on bolts and threaded parts
• AISC Specification J3.3 indicates that the
  minimum distance (s) between the centers of bolt
  holes is 2.67. A distance of 3db is preferred.
• AISC Specification J3.4 indicates that the
  minimum edge distance (Le) from the center of the
  bolt to the edge of the connected part is given
  in Table J3.4. Table J3.4 specifies minimum edge
  distances for sheared edges, edges of rolled
  shapes, and gas cut edges.

34
AISC Design Provisions

• AISC Specification indicates that the maximum
  edge distance for bolt holes is 12 times the
  thickness of the connected part (but not more
  than 152 mm). The maximum spacing for bolt holes
  is 24 times the thickness of the thinner part
  (but not more than 305 mm).
• Specification J3.6 indicates that the design
  tension or shear strength of bolts is ?FnAb
• ? 0.75
• Table J3.2, gives the values of Fn
• Ab is the unthreaded area of bolt.
• In Table J3.2, there are different types of bolts
  A325 and A490.

35
AISC Design Provisions

• The shear strength of the bolts depends on
  whether threads are included or excluded from the
  shear planes. If threads are included in the
  shear planes then the strength is lower.
• We will always assume that threads are included
  in the shear plane, therefore less strength to be
  conservative.
• We will look at specifications J3.7 J3.9 later.
• AISC Specification J3.10 indicates the bearing
  strength of plates at bolt holes.
• The design bearing strength at bolt holes is ?Rn
• Rn 1.2 Lc t Fu 2.4 db t Fu -
  deformation at the bolt holes is a design
  consideration

36
Common bolt terminologies

• A325-SC slip-critical A325 bolts
• A325-N snug-tight or bearing A325 bolts with
  thread included in the shear planes.
• A325-X - snug-tight or bearing A325 bolts with
  thread excluded in the shear planes.
• Gage center-to-center distance of bolts in
  direction perpendicular to
• members axis
• Pitch ...parallel to members axis
• Edge Distance Distance from
• center of bolt to adjacent
• edge of a member

p
37
Ex. 6.1 - Design Strength

• Calculate and check the design strength of the
  simple connection shown below. Is the connection
  adequate for carrying the factored load of 300
  kN.

10 mm
120x15 mm
30 mm
60 mm
63 k
300 kN
30 mm
20 mm A325-N bolts
30 mm
60 mm
30 mm
38
Ex. 6.1 - Design Strength

• Step I. Shear strength of bolts
• The design shear strength of one bolt in shear
  ?Fn Ab 0.75 x 330 x p x 202/4000 77.8 kN
• ? Fn Ab 77.8 kN per bolt (See Table J3.2)
• Shear strength of connection 4 x 77.8 311.2
  kN

39
Ex. 6.1 - Design Strength

• Step II. Minimum edge distance and spacing
  requirements
• See Table J3.4M, minimum edge distance 26 mm
  for rolled edges of plates
• The given edge distances (30 mm) gt 26 mm.
  Therefore, minimum edge distance requirements are
  satisfied.
• Minimum spacing 2.67 db 2.67 x 20 53.4 mm.
• (AISC Specifications J3.3)
• Preferred spacing 3.0 db 3.0 x 20 60 mm.
• The given spacing (60 mm) 60 mm. Therefore,
  spacing requirements are satisfied.

40
Ex. 6.1 - Design Strength

• Step III. Bearing strength at bolt holes.
• Bearing strength at bolt holes in connected part
  (120x15 mm plate)
• At edges, Lc 30 hole diameter/2 30 (20
  1.6)/2 19.2
• ?Rn 0.75 x (1.2 Lc t Fu) 0.75 x (1.2 x19.2
  x15x400)/1000 103.7 kN
• But, ?Rn 0.75 (2.4 db t Fu) 0.75 x (2.4 x
  20x15x400)/1000 216 kN
• Therefore, ?Rn 103.7 kN at edge holes.
• At other holes, s 60 mm, Lc 60 (20 1.6)
  38.4 mm.
• ?Rn 0.75 x (1.2 Lc t Fu) 0.75x(1.2 x 38.4 x15
  x400)/1000 207.4 kN
• But, ?Rn 0.75 (2.4 db t Fu) 216 kN. Therefore
  ?Rn 207.4 kN

41
Ex. 6.1 - Design Strength

• Therefore, ?Rn 216 kN at other holes
• Therefore, bearing strength at holes 2 x 103.7
  2 x 207.4 622.2 kN
• Bearing strength at bolt holes in gusset plate
  (10 mm plate)
• At edges, Lc 30 hole diameter/2 30 (20
  1.6)/2 19.2 mm.
• ?Rn 0.75 x (1.2 Lc t Fu) 0.75 x (1.2 x 19.2 x
  10 x 400)/1000 69.1 kN
• But, ?Rn 0.75 (2.4 db t Fu) 0.75 x (2.4 x 20
  x 10 x 400)/1000 144 kN.
• Therefore, ?Rn 69.1 kN at edge holes.

42
Ex. 6.1 - Design Strength

• At other holes, s 60 mm, Lc 60 (20 1.6)
  38.4 mm.
• ?Rn 0.75 x (1.2 Lc t Fu) 0.75 x (1.2 x 38.4 x
  10x 400)/1000 138.2 kN
• But, ?Rn 0.75 (2.4 db t Fu) 144 kN
• Therefore, ?Rn 138.2 kN at other holes
• Therefore, bearing strength at holes 2 x 69.1
  2 x 138.2 414.6 kN
• Bearing strength of the connection is the smaller
  of the bearing strengths 414.6 kN

43
Ex. 6.1 - Design Strength
Connection Strength
Shear strength 311.2
Bearing strength (plate) 622.2 kN
Bearing strength (gusset) 414.6 kN
Connection strength (fRn) gt applied factored
loads (gQ). 311.2 gt 300 Therefore ok.

• Only connections is designed here
• Need to design tension member and gusset plate

44
Eccentrically-Loaded Bolted Connections
CG
CG

• Eccentricity in the plane of the faying surface
• Direct Shear Additional Shear due to moment Pe

Eccentricity normal to the plane of the faying
surface Direct Shear Tension and Compression
(above and below neutral axis)
45
Forces on Eccentrically-Loaded Bolts

• Eccentricity in the plane of the faying surface
• LRFD Spec. presents values for computing design
  strengths of individual bolt only. To compute
  forces on group of bolts that are eccentrically
  loaded, there are two common methods
• Elastic Method Conservative. Connected parts
  assumed rigid. Slip resistance between
  connected parts neglected.
• Ultimate Strength Method (or Instantaneous Center
  of Gravity Method) Most realistic but tedious to
  apply

46
Forces on Eccentrically-Loaded Bolts with
Eccentricity on the Faying Surface

• Elastic Method
• Assume plates are perfectly rigid and bolts
  perfectly elastic ? rotational displacement at
  each bolt is proportional to its distance from
  the CG ? stress is greatest at bolt farthest from
  CG

47
Forces on Eccentrically-Loaded Bolts with
Eccentricity on the Faying Surface

• MCG Pe r1d1 r2d2 r3d3
• Since the force on each bolt is proportional to
  its distance from the CG
• Substitute into eqn. for MCG

48
Forces on Eccentrically-Loaded Bolts with
Eccentricity on the Faying Surface

• Total Forces in Bolt i
• Horizontal Component
• Vertical Component

49
Ex. 6.3 Eccentric Connections Elastic Method

• Determine the force in the most stressed bolt of
  the group using elastic method

P140 kN
e
125 mm

Eccentricity wrt CG e 125 50 175
mm Direct Shear in each bolt P/n 140/8
17.5 kN Note that the upper right-hand and the
lower right-hand bolts are the most stressed
(farthest from CG and consider direction of
forces)
100 mm
100 mm
100 mm
100 mm
50
Ex. 6.3 Eccentric Connections Elastic Method

• Additional Shear in the upper and lower
  right-hand bolts due to moment M Pe 140x175
  24500 kN.mm
• The forces acting on the upper right-hand bolt
  are as follows
• The resultant force on this bolt is

30.6 kN
10.2 kN
17.5 kN
51
Forces on Eccentrically-Loaded Bolts

• Eccentricity Normal to Plane of Faying Surface
• (a) Neutral Axis at CG

Shear force per bolt due to concentric force
Pu ruv Pu/n n of bolts Bolts above NA
are in tension. Bolts below NA are in
compression. Tension force per bolt rut
(Pue)/ndm n of bolts above NA dm moment arm
between resultant tensile and compressive forces
52
Forces on Eccentrically-Loaded Bolts

• Eccentricity Normal to Plane of Faying Surface
• (b) Neutral Axis Not at CG

Bolts above NA resist tension Bearing stress
below NA resist compression

• Shear per bolt due to concentric force Pu
• ruv Pu/n
• Select first trial location of NA as 1/6 of the
  total bracket depth.
• Effective width of the compression block
• beff 8tf bf (for W-shapes, S-shapes, welded
  plates and angles)

2rut
NA
53
Forces on Eccentrically-Loaded Bolts

• Check location of NA by equating the moment of
  the bolt area above the NA with the moment of the
  compression block area below the NA
• ?Ab x y beff x d x d/2
• ?Ab sum of areas of bolts above the NA
• y distance from X-X to the CG of bolts above
  NA
• d depth of compression block (adjust until
  satisfy)
• Once the NA has been located, the tensile force
  per bolt
• rut (PuecAb)/Ix
• c distance from NA to most remote bolt in
  group
• Ix combined moment of inertia of bolt group
  and compression block
• about NA

54
Bolts Subjected to Shear and Tension

• Nominal Tension Stress Ft of a bolt subjected to
  combined factored shear stress (fv Vu/NbAb) and
  factored tension stress (ft Tu/NbAb) can be
  computed as functions of fv as
• ? 0.75
• Fnt nominal tensile strength modified to
  include the effect of shear
• Fnt nominal tensile strength from Table J3.2 in
  (AISC Spec.)
• Fnv nominal shear strength from Table J3.2 in
  (AISC Spec.)
• fv the required shear stress

Fnt (MPa)
Bolt Type
620
A325
780
A490
55
Ex. 6.5 Combined Tension shear

• Is the bearing-type connection below
  satisfactory for the combined tension and shear
  loads shown?
• Shear stress per bolt fv Vu/NbAb537000/(8x38
  0) 176.6 MPa
• ?Fnv(0.75)(413)310 MPagt fv 176.6 MPa (OK)
• 
  Tension stress per bolt
• ft
  Tu/NbAb1073000/(8x380) 353 MPa
• 
  Nominal Tension Strength Ft (Table J3.5)
• ?Ft 0.75(1.3x620
  (620/310)x176.6) 620
• 496 MPa 620
• 496 MPa gt ft 353 MPa (OK)

1
2
56
Simple Welded Connections

• Structural welding is a process by which the
  parts that are to be connected are heated and
  fused, with supplementary molten metal at the
  joint.
• A relatively small depth of material will become
  molten, and upon cooling, the structural steel
  and weld metal will act as one continuous part
  where they are joined.

P
P
P
P
57
Introductory Concepts
Welding Process Fillet Weld
58
Introductory Concepts

• The additional metal is deposited from a special
  electrode, which is part of the electric circuit
  that includes the connected part.
• In the shielded metal arc welding (SMAW) process,
  current arcs across a gap between the electrode
  and the base metal, heating the connected parts
  and depositing part of the electrode into the
  molten base metal.
• A special coating on the electrode vaporizes and
  forms a protective gaseous shield, preventing the
  molten weld metal from oxidizing before it
  solidifies.
• The electrode is moved across the joint, and a
  weld bead is deposited, its size depending on the
  rate of travel of the electrode.

59
Introductory Concepts

• As the weld cools, impurities rise to the
  surface, forming a coating called slag that must
  be removed before the member is painted or
  another pass is made with the electrode.
• Shielded metal arc welding is usually done
  manually and is the process universally used for
  field welds.
• For shop welding, an automatic or semi automatic
  process is usually used. Foremost among these is
  the submerged arc welding (SAW),
• In this process, the end of the electrode and the
  arc are submerged in a granular flux that melts
  and forms a gaseous shield. There is more
  penetration into the base metal than with
  shielded metal arc welding, and higher strength
  results.

60
Introductory Concepts

• Other commonly used processes for shop welding
  are gas shielded metal arc, flux cored arc, and
  electro-slag welding.
• Quality control of welded connections is
  particularly difficult, because defects below the
  surface, or even minor flaws at the surface, will
  escape visual detection. Welders must be properly
  certified, and for critical work, special
  inspection techniques such as radiography or
  ultrasonic testing must be used.

61
Introductory Concepts

• The two most common types of welds are the fillet
  weld and the groove weld. Fillet weld examples
  lap joint fillet welds placed in the corner
  formed by two plates
• Tee joint fillet welds placed at the
  intersection of two plates.
• Groove welds deposited in a gap or groove
  between two parts to be connected
• e.g., butt, tee, and corner joints with beveled
  (prepared) edges
• Partial penetration groove welds can be made from
  one or both sides with or without edge
  preparation.

62
Welded Connections

• Classification of welds
• According to type of weld
• According to weld position
• According to type of joint
• Butt, lap, tee, edge or corner
• According to the weld process
• SMAW, SAW

Groove weld
Fillet weld
Flat, Horizontal, vertical or overhead weld
63
Introductory Concepts
64
Weld Limit States

• The only limit state of the weld metal in a
  connection is that of fracture
• Yielding is not a factor since any deformation
  that might take place will occur over such a
  short distance that it will not influence the
  performance of the structure

65
Design of Welded Connections

• Fillet welds are most common and used in all
  structures.
• Weld sizes are specified in 1 mm increments
• A fillet weld can be loaded in any direction in
  shear, compression, or tension. However, it
  always fails in shear.
• The shear failure of the fillet weld occurs along
  a plane through the throat of the weld, as shown
  in the Figure below.

66
Design of Welded Connections
hypotenuse
root
L length of the weld a size of the weld
67
Design of Welded Connections

• Shear stress in fillet weld of length L subjected
  to load P
• fv If the ultimate shear
  strength of the weld fw
• Rn
• ?Rn i.e., ? factor 0.75
• fw shear strength of the weld metal is a
  function of the electrode used in the SMAW
  process.
• The tensile strength of the weld electrode can be
  413, 482, 551, 620, 688, 758, or 827 MPa.
• The corresponding electrodes are specified using
  the nomenclature E60XX, E70XX, E80XX, and so on.
  This is the standard terminology for weld
  electrodes.

68
Design of Welded Connections

• The two digits "XX" denote the type of coating.
• The strength of the electrode should match the
  strength of the base metal.
• If yield stress (?y) of the base metal is ? 413 -
  448 MPa, use E70XX electrode.
• If yield stress (?y) of the base metal is ? 413 -
  448 MPa, use E80XX electrode.
• E70XX is the most popular electrode used for
  fillet welds made by the SMAW method.

E electrode 70 tensile strength of electrode
(ksi) 482 MPa XX type of coating
69
Fillet Weld

• Stronger in tension and compression than in shear
• Fillet weld designations
• 12 mm SMAW E70XX fillet weld with equal leg
  size of 12 mm, formed using Shielded Metal Arc
  Welding Process, with filler metal electrodes
  having a minimum weld tensile strength of 70 ksi.
• 9 mm-by-12 mm SAW E110XX fillet weld with
  unequal leg sizes, formed by using Submerged Arc
  Metal process, with filler metal electrodes
  having a minimum weld tensile strength of 758 MPa.

Unequal leg fillet weld
70
Fillet Weld Strength

• Stress in fillet weld factored load/eff. throat
  area
• Limit state of Fillet Weld is shear fracture
  through the throat, regardless of how it is
  loaded
• Design Strength
• For equal leg fillet weld

71
Design of Welded Connections

• Table J2.5 in the AISC Specifications gives the
  weld design strength
• fw 0.60 FEXX
• For E70XX, ?fw 0.75 x 0.60 x 482 217 MPa
• Additionally, the shear strength of the base
  metal must also be considered
• ?Rn 0.9 x 0.6 Fy x area of base metal subjected
  to shear
• where, Fy is the yield strength of the base metal.

72
Design of Welded Connections

• For example

• Strength of weld in shear 0.75 x 0.707 x a x
  Lw x fw
• In weld design problems it is advantageous to
  work with strength per unit length of the weld or
  base metal.

73
Limitations on Weld Dimensions

• Minimum size (amin)
• Function of the thickness of the thinnest
  connected plate
• Given in Table J2.4 in the AISC specifications
• Maximum size (amax)
• function of the thickness of the thinnest
  connected plate
• for plates with thickness ? 6 mm, amax 6 mm.
• for plates with thickness ? 6 mm, amax t 2
  mm.
• Minimum length (Lw)
• Length (Lw) ? 4 a otherwise, aeff Lw / 4 a
  weld size
• Read J2.2 b page 16.1-95
• Intermittent fillet welds Lw-min 4 a and 38
  mm.

74
Limitations on Weld Size AISC Specifications
J2.2b Page 16.1-95

• The minimum length of fillet weld may not be less
  than 4 x the weld leg size. If it is, the
  effective weld size must be reduced to ¼ of the
  weld length
• The maximum size of a fillet weld along edges of
  material less than 6 mm thick equals the material
  thickness. For material thicker than 6 mm, the
  maximum size may not exceed the material
  thickness less 2 mm. (to prevent melting of base
  material)
• The minimum weld size of fillet welds and minimum
  effective throat thickness for partial-penetration
  groove welds are given in LRFD Tables J2.4 and
  J2.3 based on the thickness of the base materials
  (to ensure fusion and minimize distortion)
• Minimum end return of fillet weld ? 2 x weld size

75
Limitations on Weld Dimensions

• Maximum effective length - read AISC J2.2b
• If weld length Lw lt 100 a, then effective weld
  length (Lw-eff) Lw
• If Lw lt 300 a, then effective weld length
  (Lw-eff) Lw (1.2 0.002 Lw/a)
• If Lw gt 300 a, the effective weld length (Lw-eff)
  0.6 Lw
• Weld Terminations - read AISC J2.2b
• Lap joint fillet welds terminate at a distance
  gt a from edge.
• Weld returns around corners must be gt 2 a

76
Guidelines for Fillet Weld design

• Two types of fillet welds can be used
• Shielded Metal Arc Welding (SMAW)
• Automatic Submerged Arc Welding (SAW)

Shear failure plane
AISC Section J2.2
77
Weld Symbols (American Welding Society AWS)

• Fillet weld on arrow side. Welds leg size is 10
  mm. Weld size is given to the left of the weld
  symbol. Weld length (200 mm) is given to the
  right of the symbol
• Fillet weld, 12 mm size and 75 mm long
  intermitten welds 125 on center, on the far side
• Field fillet welds, 6 mm in size and 200 mm
  long, both sides.
• Fillet welds on both sides, staggered
  intermitten 10 mm in size, 50 mm long and 150 mm
  on center
• Weld all around joint
• Tail used to reference certain specification or
  process

10
200
12
75_at_125
6
200
10
50_at_150
78
Guidelines for Fillet Weld design

• Fillet weld design can be governed by the smaller
  value of
• Weld material strength
• Base Metal Strength

Yield Limit State
AISC Table J2.5
79
Guidelines for Fillet Weld design

• The weld strength will increase if the force is
  not parallel to the weld

• Maximum weld size

• Minimum weld size

AISC Table J2.4
80
Capacity of Fillet Weld

• The weld strength is a function of the angle q

Strength
w weld size
Angle (q)
81
Ex. 7.6 Design Strength of Welded Connection

• Determine the design strength of the tension
  member and connection system shown below. The
  tension member is a 100 mm x 10 mm thick
  rectangular bar. It is welded to a 15 mm thick
  gusset plate using E70XX electrode. Consider the
  yielding and fracture of the tension member.
  Consider the shear strength of the weld metal and
  the surrounding base metal.

t 15 mm
a 6 mm
100 mm x 10 mm
125 mm
12 mm
12 mm
125 mm
82
Ex. 7.6 Design Strength of Welded Connection

• Step I. Check for the limitations on the weld
  geometry
• tmin 10 mm (member)
• tmax 15 mm (gusset)
• Therefore, amin 5 mm - AISC Table J2.4
• amax 10 mm 2 mm 8 mm - AISC J2.2b page
  16.1-95
• Fillet weld size a 6 mm - Therefore, OK!
• Lw-min 4 x 6 24 mm and 38 mm - OK.
• Lw-min for each length of the weld 100 mm
  (transverse distance between welds, see J2.2b)
• Given length 125 mm, which is gt Lmin.
  Therefore, OK!

83
Ex. 7.6 Design Strength of Welded Connection
84
Ex. 7.6 Design Strength of Welded Connection

• Length/weld size 125/6 20.8 - Therefore,
  maximum effective length J2.2 b satisfied.
• End returns at the edge corner size - minimum 2
  a 12 mm -Therefore, OK!
• Step II. Design strength of the weld
• Weld strength ?x 0.707 x a x 0.60 x FEXX x Lw
• 0.75 x 0.707 x 6 x 0.60 x 482 x
  250/1000
• 230 kN
• Step III. Tension strength of the member
• ?Rn 0.9 x 344 x 100 x 10/1000 310 kN -
  tension yield

85
Ex. 7.6 Design Strength of Welded Connection

• ?Rn 0.75 x Ae x 448 - tension fracture
• Ae U A
• Ae Ag 100 x 10 1000 mm
• Therefore, ?Rn 336 kN
• The design strength of the member-connection
  system 230 kN. Weld strength governs. The end
  returns at the corners were not included in the
  calculations.

86
Elastic Analysis of Eccentric Welded Connections

• It is assumed here that the rotation of the weld
  at failure occur around the elastic centre (EC)
  of the weld. The only difference from bolts is we
  are dealing with unit length of weld instead of a
  bolt

• The shear stress in weld due to torsion moment M
  is

• M is the moment, d is the distance from the
  centroid of the weld to the weld point where we
  evaluate the stress, J is the polar moment of
  inertia of the weld

AISC Manual Part 8
87
Elastic Analysis of Eccentric Welded Connections
Shear Torsion

• stresses due to torsional moment M is

- Calculation shall be done for teff
- Or for teff 1 mm
88
Elastic Analysis of Eccentric Welded Connections
Shear Torsion

• Forces due to direct applied force is

• Total stress in the weld is

89
Ex. 7.7 Design Strength of Welded Connection
Shear and Torsion
250 mm

• Determine the size of weld required for the
  bracket connection in the figure. The service
  dead load is 50 kN, and the service live load is
  120 kN. A36 steel is used for the bracket, and
  A992 steel is used for the column.

D 50 kN L 120 kN
300 mm
15 mm PL
200 mm
Calculations are done for teff 25 mm
90
Ex. 7.7 Design Strength of Welded Connection
Shear and Torsion

• Step I Calculate the ultimate load
• Pu 1.2D 1.6L 1.2(50)1.6(120) 252 kN
• Step II Calculate the direct shear stress
• Step III Compute the location of the centroid
  
• Step IV Compute the torsional moment
• e 250 200 57.1 392.9 ? M Pe
  252(392.9)99011 kN-mm.

91
Ex. 7.7 Design Strength of Welded Connection
Shear and Torsion

• Step V Compute the moments of inertia of the
  total weld area
• Ix 1(300)3 (1/12)2(200)(150)211.25106 mm4
• Iy 2 (200)3 (1/12)(200)(100-57.1)2
  300(57.1)23.05106 mm4
• J Ix Iy (11.25 3.05)106 14.3106 mm4
• Step VI Compute stresses at critical location

92
Ex. 7.7 Design Strength of Welded Connection
Shear and Torsion

• Step VII Check the shear strength of the base
  metal
• The shear yield strength of the angle leg is
• FRn (0.9)0.6Fyt 0.9(0.6)(248)(15) 2009
  N/mm
• The base metal shear strength is therefore
• 2009 N/mm gt 1703 N/mm (OK).
• Step VIII Calculate the weld size, assuming Fw
  0.6FEXX
• ? Use 12 mm
• Answer Use a 12-mm fillet weld, E70 electrode.

93
Elastic Analysis of Eccentric Welded Connections
Shear Tension
94
Elastic Analysis of Eccentric Welded Connections
Shear Tension

• stresses due to torsion moment M is

- Calculation shall be done for teff
- Or for teff 1 mm

• F applied force
• e eccentricity of load
• Ix moment of inertia around x-axis
• c distance from neutral axis of weld to the
  farthest weld point

95
Ex. 7.8 Design Strength of Welded Connection
Shear Tension

• An L6x4x1/2 is used in a seated beam connection,
  as shown in the figure. It must support a service
  load reaction of 25 kN dead load and a 50 kN
  live load. The angles are A36 and the columns in
  A992. E70XX electrodes are to be used. What size
  fillet weld are required for the connection to
  the column flange?

152 mm
20 mm
20 mm
82 mm
96
Ex. 7.8 Design Strength of Welded Connection
Shear Tension

• Step I calculate the eccentricity of the
  reaction with respect to the weld is
• e 20 82/2 61 mm
• Step II Calculate the moment of inertia for the
  weld configuration
• I 2(1)(152)3 / 12 585300 mm4 c 152/2
  76 mm
• Step III Calculate the factored-load reaction
  is
• Pu 1.2D 1.6L 1.2(25)1.6(50) 110 kN
• Mu Pue 110(61) 6710 kN-mm

97
Ex. 7.8 Design Strength of Welded Connection
Shear Tension

• Step III Calculate the factored-load reaction
  is

• Step IV The required weld size a
• a 943/(0.9x0.707x0.6x482) 6.2 mm

98
Ex. 7.8 Design Strength of Welded Connection
Shear Tension

• The required size is therefore a 7 mm
• Step V Check minimum and maximum weld size
• From AISC Table J2.4 ? Minimum weld size 5 mm
• From AISC Table J2.2b ? Maximum weld size 13 -
  2 11 mm
• Try a 7 mm
• Step VI Check the shear capacity of the base
  metal (the angle controls)
• Applied direct shear fv 362 N/mm
• The shear yield strength of the angle leg is
• FRn 0.90.6Fyt (0.9)0.6(248)(13) 1741
  N/mm
• The base metal shear strength is therefore
• 1741 N/mm gt 362 N/mm (OK).

99
Ultimate Strength Analysis of Eccentric Welded
Connections

• When comparing elastic analysis to experimental
  on eccentric welded connections, it becomes
  obvious that elastic analysis is over
  conservative.

100
Ultimate Strength Analysis of Eccentric Welded
Connections

• Similar to bolts, weld can be divided into
  segments which rotate about an instantaneous
  centre (IC)
• Instead of summing the forces we can integrate
  over the length of the weld to get the basic
  equations of equilibrium

Thus
101
Ultimate Strength Analysis of Eccentric Welded
Connections

• However, in weld The force in each segment R
  is also function of the angle q between the force
  direction and the weld.

Deformation of the segment
Deformation of the segment at max stress
- Similar to bolts, the far weld element might
have a higher proportion of force.
102
Ultimate Strength Analysis of Eccentric Welded
Connections
However, the critical weld is that of the
smallest Dm/rs
Determine the segment that has
The ultimate deformation Du happens for the
segment with smallest Dm/rs
103
Ultimate Strength Analysis of Eccentric Welded
Connections
In all equations q is in radian ranges from
zero to p/2
104
Ultimate Strength Analysis of Eccentric Welded
Connections

• Thus to estimate the force in the critical
  segment we do the following steps
• 1- Divide the weld into segments and assume an
  IC
• 2- Calculate the deformation of each element
• 3- Compute the ratio Dm/r and determine rcrit
• 4- For this critical segment compute the ultimate
  deformation Du
• 5- Compute the deformation of each other segment

105
Ultimate Strength Analysis of Eccentric Welded
Connections

• Steps continued
• 6- Compute the stress in each segment
• 7- Check equilibrium equations

106
Extra Slides
107
Slip-critical Bolted Connections

• High strength (A325 and A490) bolts can be
  installed with such a degree of tightness that
  they are subject to large tensile forces.
• These large tensile forces in the bolt clamp the
  connected plates together. The shear force
  applied to such a tightened connection will be
  resisted by friction as shown in the Figure below.

108
Slip-critical Bolted Connections
109
Slip-critical Bolted Connections

• Thus, slip-critical bolted connections can be
  designed to resist the applied shear forces using
  friction. If the applied shear force is less than
  the friction that develops between the two
  surfaces, then no slip will occur between them.
• However, slip will occur when the friction force
  is less than the applied shear force. After slip
  occurs, the connection will behave similar to the
  bearing-type bolted connections designed earlier.
• Table J3.1 summarizes the minimum bolt tension
  that must be applied to develop a slip-critical
  connection.

110
Slip-Critical Connections

• Loads to be transferred ? Frictional Resistance
  (tension force in bolt x coefficient of friction
  ?) ? No slippage between members
• ? No bearing and shear stresses in bolt
• LRFD J3.10 requires bearing strength to be
  checked for both Bearing-Type connections and
  Slip-Critical connections (even though there is
  supposed to be little or no bearing stresses on
  the bolts in Slip-Critical connections)

111
Slip-critical Bolted Connections

• The shear resistance of fully tensioned bolts to
  slip at factored loads service loads is given
  by AISC Specification J3.8
• Shear resistance at factored load ?Rn ?(1.13
  ?hscTb Ns)
• ? - 0.85 for factored loads 1.00 for service
  loads
• ? - friction coefficient
• Tb - minimum bolt tension given in Table J3.1
• hsc hole factor determined as
• For standrad size holes hsc 1.0
• For oversized and short-slotted holes hsc
  0.85
• For long-slotted holes hsc 0.7
• Ns - number of slip planes

112
Slip-Critical Connections

• Slip Coefficients (LRFD J3.8)

Surface ?
Class A (unpainted clean mill scale or surfaces with class A coating on blast-cleaned steel) Class B (unpainted blast-cleaned surfaces or surfaces with Class B coating on blast-cleaned steel 0.35 0.50
113
Slip-critical Bolted Connections

• When the applied shear force exceeds the ?Rn
  value stated above, slip will occur in the
  connection.
• The final strength of the connection will depend
  on the shear strength of the bolts and on the
  bearing strength of the bolts. This is the same
  strength as that of a bearing type connection.
• Slip critical connections shall still be checked
  as bearing type in case slip occurs as a result
  of overload.

114
Ex. 6.2 - Slip-critical Connections

• Design a slip-critical splice for a tension
  member subjected to 600 kN of tension loading.
  The tension member is a W8 x 28 section made from
  A36 material. The unfactored dead load is equal
  to 100 kN and the unfactored live load is equal
  to 300 kN. Use A325 bolts. The splice should be
  slip-critical at service loads.

115
Ex. 6.2 - Slip-critical Connections

• Step I. Service and factored loads
• Service Load D L 400 kN.
• Factored design load 1.2 D 1.6 L 600 kN
• Tension member is W8 x 28 section made from A36
  steel. The tension splice must be slip critical
  (i.e., it must not slip) at service loads.
• Step II. Slip-critical splice connection (service
  load)
• ?Rn of one fully-tensioned slip-critical bolt
  ?(1.13 ?hscTb Ns)
• (See Spec. J3.8)

116
Ex. 6.2 - Slip-critical Connections

• Assume db 20 mm.
• ?Rn of one bolt 1.0 x 1.13 x 0.35 x 1.0x142x1
  56.2 kN
• Note, Tb 142 kN from Table J3.1M
• ?Rn of n bolts 56.2 x n gt 400 kN (splice must
  be slip-critical at service)
• Therefore, n gt 7.12

117
Ex. 6.2 - Slip-critical Connections

• Step III. Layout of splice connection
• Flange-plate splice connection

118
Ex. 6.2 - Slip-critical Connections

• To be symmetric about the centerline, need the
  number of bolts to be a multiple of 8.
• Therefore, choose 16 fully tensioned 20 mm A325
  bolts with layout as shown above.
• Minimum edge distance (Le) 34 mm from Table
  J3.4M
• Design edge distance Le 40 mm.
• Minimum spacing s (22/3) db 2.67 x 20
  53.4 mm. (Spec. J3.3)
• Preferred spacing s 3.0 db 3.0 x 20 60 mm
  (Spec. J3.3)
• Design s 60 mm.
• Assume 10 mm thick splice plate

119
Ex. 6.2 - Slip-critical Connections

• Step IV. Connection strength at factored loads
• The splice connection should be designed as a
  normal shear/bearing connection beyond this point
  for the factored load of 600 kN.
• Shear strength of a bolt 77.8 kN (see Example
  7.1)
• The shear strength of bolts 77.8 kN/bolt x 8
  622.4 kN
• Bearing strength of 20 mm bolts at edge holes (Le
  30 mm) 69.1 kN (see Example 7.1)
• Bearing strength of 20 mm bolts at non-edge holes
  (s 60 mm) 138.2 kN (see Example 7.1)
• Bearing strength of bolt holes in flanges of wide
  flange section
• 4 x 69.1 4 x 138.2 829.2 kN gt 600 kN OK

120
Ex. 6.2 - Slip-critical Connections

• Step V. Design the splice plate
• Tension yielding 0.9 Ag Fy gt 300 kN Therefore,
  Ag gt 1344 mm2
• Tension fracture 0.75 An Fu gt 300 kN
• Therefore, An Ag - 2 x (20 3.2) x 10 gt 1000
  mm2
• Beam flange width 166 mm
• Assume plate width 160 mm x 10 mm which has Ag
  1660 mm2
• Step VI. Check member strength
• Student on his/her own.

121
Ultimate Strength Analysis of Eccentric Bolted
Connections

• Experimental study by Crawford and Kulak (1971)
  showed

- The load-deformation relationship of any bolt
is non-linear
AISC Manual Part 7
122
Ultimate Strength Analysis of Eccentric Bolted
Connections

• The following conclusions were also shown
• Failure rotation does not happen around the
  elastic center but around an instantaneous centre
  (IC)
• The IC does not coincide with the EC
• The deformation of each bolt is proportional to
  its distance from the IC
• Similar to the elastic analysis, the connection
  capacity is governed by the force in the farthest
  bolt

123
Ultimate Strength Analysis of Eccentric Bolted
Connections
Measured at the elastic centroid

• At failure

Eqn (1)

Eqn (2)

Eqn (3)
124
Ultimate Strength Analysis of Eccentric Bolted
Connections

• Therefore, getting the maximum force in the
  farthest bolt requires determining the unknown
  e
• Because of the non-linear relationship, e can be
  determined by trial and error
• A spreadsheet can be used to determine e

125
Forces on Eccentrically-Loaded Bolts with
Eccentricity on the Faying Surface

• Ultimate Strength Method (Instantaneous Center of
  Rotation Method)
• R Rult(1
  e-0.394?)0.55

• R Nominal shear strength of 1 bolt at a
  deformation ?, k
• Rult Ultimate shear strength of 1 bolt, kN
• Total deformation, including shear, bearing and
  bending deformation in the bolt and bearing
  deformation of the connected elements, in. (?max
  8.6 mm for 20 mm ASTM A325 bolt)
• ?1/d1 ?2/d2 ?max/dmax
• e 2.718base of the natural logarithm

126
Ultimate Strength Method (Instantaneous Center of
Rotation Method)

• Trial and error
• Assume e
• Compute ?i di?max/dmax (?max is assumed for
  bolt at farthest distance from IC)
• Compute RiRult(1- e-0.394?i)0.55
• Check for Pu(? Rd)/(ee)
• If not satisfied, repeat with another e

127
Ex. 6.4 Eccentric Connections Ultimate Method

• Determine the largest eccentric force Pu for
  which the design shear strength of the bolts in
  the connection is adequate using the IC method.
  Use bearing-type 20 mm A325X bolts

Pu
e 100 mm
e60 mm

• - Design shear strength per bolt (Ex. 7-1)
• Ru ? Rn 77.8 kN
• After several trials, assume e 60 mm. Bolts 2
  and 4 are furthest from the IC, therefore ?2 ?4
  ?max 8.6 mm
• Compute ?i and Ri in tabulated form

75 mm
d1
d2
75 mm
d4
d3
75 mm
128
Ex. 6.4 Eccentric Connections Ultimate Method
Bolt h (mm) v (mm) d (mm) ? (mm) R (kN) Ry (kN) Rd (kN.mm)
1 22.5 75 78.3 5.47 72.7 20.9 5692
2 97.5 75 123 8.6 77.8 61.67 7585
3 22.5 75 78.3 5.47 72.7 20.9 5692
4 97.5 75 123 8.6 77.8 61.67 7585
? 165.14 ? 26554
Check Pu (?Rd)/(ee) (26554/(60100))
166 kN ?Ry 165.14 kN (OK)