Retrofit of Steel Moment Frame Connections: Current Testing Program

1
Teaching Modules for Steel Instruction
Tension Member THEORY SLIDES
Developed by Scott Civjan University of
Massachusetts, Amherst
2

• Tension Members
• Chapter D Tension Member Strength
• Chapter B Gross and Net Areas
• Chapter J Block Shear
• Part 5 Design Charts and Tables

3

• Gross and Net Areas
• Criteria in Table B3.13
• Strength criteria in Chapter D Design of Members
  for Tension

4
Yield on Gross Area ft0.90 (Wc1.67)
Fracture on Effective Net Area ft0.75 (Wc2.00)
Block Shear ft0.75 (Wc2.00)
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Yielding on Gross Area Ag
6
Yield on Gross Area
PnFyAg Equation D2-1
ft0.90 (Wc1.67)
Ag Gross Area Total cross-sectional area in the
plane perpendicular to tensile stresses
7
Fracture on Effective Net Area Ae
8
Fracture on Effective Net Area
PnFuAe Equation D2-2
ft0.75 (Wc2.00)
Ae Effective Net Area Accounts for any holes or
openings, potential failure planes not
perpendicular to the tensile stresses, and
effects of shear lag
9
Fracture on Effective Net Area
If holes are included in the cross section less
area resists the tension force
Bolt holes are larger than the bolt diameter
In addition processes of punching or drilling
holes can damage the steel around the perimeter
10
Fracture on Effective Net Area
Holes or openings
Section D3.2 Account for 1/16 greater than bolt
hole size shown in Table J3.3 Accounts for
potential damage in fabrication
11
Fracture on Effective Net Area
An Net Area Modify gross area (Ag) to account
for the following
Holes or openings
Potential failure planes not perpendicular to the
tensile stresses
12
Fracture on Effective Net Area
Design typically uses average stress values
This assumption relies on the inherent ductility
of steel
Therefore average stresses are typically used in
design
13
Fracture on Effective Net Area
Similarly, bolts and surrounding material will
yield prior to fracture due to the inherent
ductility of steel
Therefore assume each bolt transfers equal force
14
Fracture on Effective Net Area
The plate will fail in the line with the highest
force (for similar number of bolts in each line)
Each bolt line shown transfers 1/3 of the total
force
Net area reduced by hole area
Pu
Cross Section
3
1
2
Bolt line
15
Fracture on Effective Net Area
The plate will fail in the line with the highest
force (for similar number of bolts in each line)
Each bolt line shown transfers 1/3 of the total
force
Bolt line 1 resists Pu in the plate Bolt line 2
resists 2/3Pu in the plate Bolt line 3 resists
1/3Pu in the plate
Force in plate
Net area reduced by hole area
Pu
1/3 Pu
2/3 Pu
0
Pu
Cross Section
3
1
2
Bolt line
16
Fracture on Effective Net Area
For a plate with a typical bolt pattern the
fracture plane is shown Yield on Ag would occur
along the length of the member Both failure
modes depend on cross-sectional areas
Yield failure (elongation) occurs along the
length of the member
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• EXAMPLE

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Fracture on Effective Net Area
What if holes are not in a line perpendicular to
the load?
Need to include additional length/Area of failure
plane due to non-perpendicular path
Additional strength depends on Geometric length
increase Combination of tension and shear
stresses Combined effect makes a direct
calculation difficult
19
Fracture on Effective Net Area
Diagonal hole pattern Additional length of
failure plane equal to s2/4g Section B3.13 and
D3.2
s longitudinal center-to-center spacing of holes
(pitch) g transverse center-to-center spacing
between fastener lines (gage)
20
Fracture on Effective Net Area
AnNet Area
AnAg-(dn)t(s2/(4g))t
number of holes intersected by failure
plane dn corrected hole diameter per B.3-13 t
thickness of tension member Other terms defined
on previous slides
21
Fracture on Effective Net Area
When considering angles
When considering angles Find gage (g) on page
1-46 Workable Gages in Standard Angles unless
otherwise noted
22

• EXAMPLE

23
Fracture on Effective Net Area
Shear Lag
Accounts for distance required for stresses to
distribute from connectors into the full cross
section
Largest influence when
Only a portion of the cross section is connected
Connection does not have sufficient length
24
Fracture on Effective Net Area
Shear Lag affects members where Only a portion
of the cross section is connected Connection does
not have sufficient length
25
Fracture on Effective Net Area
Pu
l Length of Connection
26
Fracture on Effective Net Area
Shear lag less influential when l is long, or if
outstanding leg has minimal area or eccentricity
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Fracture on Effective Net Area
Ae Effective Net Area Modify net area (An) to
account for shear lag
Ae AnU Equation D3-1
U Shear Lag Factor Reduction
Connection eccentricity
l length where force transfer occurs (distance
parallel to applied tension force along bolts or
weld)
28
Fracture on Effective Net Area
PnFuAe Equation D2-2
ft0.75 (Wc2.00)
Ae Effective Net Area Accounts for any holes or
openings, potential failure planes not
perpendicular to the tensile stresses, and
effects of shear lag
29
Fracture on Effective Net Area
AeEffective Net Area AnNet Area Ae?An Due to
Shear Lag
30
Fracture on Effective Net Area
Now consider a much wider plate
31
Fracture on Effective Net Area
This concept describes the Whitmore Section
30o
30o
32

• EXAMPLE

33
Block Shear
34
Block Shear
Failure Tears Out Block of Steel
Block Defined by Center Line of Holes Edge of
Welds
State of Combined Yielding and Fracture
Failure Planes
At Least One Each in Tension and Shear
35
Block Shear
Typical Examples in Tension Members
Angle Connected on One Leg
W-Shape Flange Connection
Plate Connection
36
Block Shear
Angle Bolted to Plate
Pu
Pu
37
Block Shear
Angle Bolted to Plate
Pu
Block Failure from Angle
Pu
Block Failure From Plate
38
Block Shear
Flange of W-Shape Bolted to Plate
Pu
First look at the W-Shape, then the plate
39
Block Shear
Flange of W-Shape Bolted to Plate
First look at the W-Shape, then the plate
40
Block Shear
Flange of W-Shape Bolted to Plate
Pu
Pu
41
Block Shear
Flange of W-Shape Bolted to Plate
Pu
Block Failure in Plate
Pu
Block Failure in Plate
42
Block Shear
Angle or Plate Welded to Plate
Pu
Weld around the perimeter
Two Block Shear Failures to Check
43
Block Shear
Angle or Plate Welded to Plate
Pu
Pu
44
Block Shear
Angle or Plate Welded to Plate
Pu
Block Failure From Plate
Pu
45
Block Shear
Block Shear Rupture Strength (Equation J4-5)
ft0.75 (Wc2.00)
Agv Gross area subject to shear Anv Net area
subject to shear Ant Net area subject to
tension Ubs 1 or 0.5 (1 for most tension
members, see Figure C-J4.2)
46

• EXAMPLE

47
Bearing at Bolt Holes
48
Bearing at Bolt Holes
Bolts bear into material around hole
Direct bearing can deform the bolt hole an
excessive amount and be limited by direct
bearing capacity
If the clear space to adjacent hole or edge
distance is small, capacity may be limited by
tearing out a section of base material at the bolt
49
Bearing at Bolt Holes
Bolt
Pu
50
Bearing at Bolt Holes
Bolt
Pu
51
Bearing at Bolt Holes
Bolt
Pu
52
Bearing at Bolt Holes
Pu
53
Bearing at Bolt Holes
Bolt
Pu
54
Bearing at Bolt Holes
Pu
55
Bearing at Bolt Holes
For standard, oversized and short-slotted hole or
long slotted hole with slot parallel to the
direction of loading (Equation J3-6a)
ft0.75 (Wc2.00)
Lc Clear distance in the direction of force t
thickness of connected material d nominal bolt
diameter Fu Specified minimum tensile strength
of the connected material
56
Bearing at Bolt Holes
Other situations have similar design equations
For the similar case, but when deformation of the
bolt hole is not a design consideration
(Equation J3-6b)
For long-slotted hole with slot perpendicular to
the direction of force (Equation J3-6c)