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N.W.F.P. University of Engineering and
Technology Peshawar
Lect ure 06: Tens ion Members
1
By: Prof Dr. Akhtar Naeem Khan
Types of Steel Structures
Introductory concepts
Top ic s t o be Addressed
Design Strength
Net Area at Connection
Shear Lag Phenomenon
CE-409: Lecture 06 Prof. Dr Akhtar Naeem Khan 2
ASD and LRFD Design of TensionMembers
Design Examples
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The form of a tension member is
Types o f s t ee l s t ruc t ures
governed to a large extent by
Type of structure of which it is a part
Method of joining it to connecting portions.
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Types o f s t ee l s t ruc t ures
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Types o f s t ee l s t ruc t ures
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Types o f s t ee l s t ruc t ures
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Types o f s t ee l s t ruc t ures
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Types o f s t ee l s t ruc t ures
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Types o f s t ee l s t ruc t ures
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Sec t ions for Tension Members
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Sec t ions for Tension Members
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Design St resses
for
Base Mat er ia l
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In t roduc t o ry Concep ts
Stress: The stress in an axially loaded tensionmember is given by Equation
The stress in a tension member is uniformthroughout the cross-section except:
near the point of application of load, and
at the cross-section with holes for bolts or other
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, .
Types o f s t ee l s t ruc t ures
b b
Gusset plate
7/8 in . diameter hole
Section b-bb b
Gusset plate
7/8 in . diameter hole
b b
Gusset plate
7/8 in . diameter hole
Section b-bSection b-b
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aa
8 x in. barSection a-a
aa
8 x in. bar
aa
8 x in. barSection a-aSection a-a
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Types o f s t ee l s t ruc t ures
b b
Gusset plate
Section b-bb b
Gusset plate
b b
Gusset plate
Section b-bSection b-b
2
aa
8 x in. bar
7/8 in. diameter hole
Section a-a
aa
8 x in. bar
7/8 in. diameter hole
aa
8 x in. bar
7/8 in. diameter hole
Section a-aSection a-a
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Area of bar at section b b = (8 2 x 7/8 ) x = 3.12 in2
The unreduced area of the member is called its gross area = AgThe reduced area of the member is called its net area = An
Design st rengt h
A tension member can fail by reaching oneof two limit states:
1. Excessive deformation Yielding at the gross area
2. Fracture Fracture at the net area
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Design st rengt h
1. Excessive deformation can occur due to theyielding of the gross section at section a-a
b b
7/8 in.
b b
7/8 in.
b b
7/8 in.
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aa
8 x
aa
8 x
aa
8 x
Design st rengt h2. Fracture of the net section can occur if the stress
at the net section (section b-b) reaches theultimate stress Fu
b b
7/8 in.
b b
7/8 in.
b b
7/8 in.
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aa
8 x
aa
8 x
aa
8 x
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Design st rengt h
Yielding of the gross section will occur whenthe stress f reaches Fy
Nominal yield strength = Pn = Ag Fy
Fracture of the net section will occur after the stress
y
g
FA
==f
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u
Nominal fracture strength = Pn = Ae Fu
u
e
FAP ==f
Design st rengt h
AISC/ASDFt = 0.6 Fy on Gross Area
Ft = 0.5 Fu on Effective Area
AISC/LRFD
Design strength for yielding on gross area
P = F A = 0.9 F A
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Design strength for fracture of net section
tPn = tFu Ae = 0.75 Fu Ae
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Ef fec t ive Net Area
The connection has a significant influence on theperformance of a tension member. A connection almost always weakens the memberand a measure of its influence is called jointefficiency.
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Ef fec t ive Net Area
Joint efficiency is a function of:
(a) Material ductility
(b) Fastener spacing
(c) Stress concentration at holes
(d) Fabrication procedure
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(e) Shear lag.
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Ef fec t ive Net AreaResearch indicates that shear lag can be accounted for by
using a reduced or effective net area Ae
CG
2x
1x
L
xU = 1
For Bolted Connections
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For bolted connection, t e effective net area is Ae = UAn
For welded connection, the effective net area is Ae = UAg
Ef fec t ive Net Area
For W, M, and S shapes with width-to-depth ratio of at least2/3 and for Tee shapes cut from them, if the connection is
the direction of applied load ,
U= 0.9
For all other shapes with at least three fasteners per line ,U= 0.85
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For all members with only two fasteners per line
U= 0.75
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Net Area Ex ampleExample : A 5 x bar of A572 Gr. 50 steel is used as a tension
member. It is connected to a gusset plate with six 7/8 in. diameterbolts as shown in below. Assume that the effective net area Ae equals
the actual net area A and com ute the tensile desi n stren th of thenmember.
b b
Gusset plate
7/8 in. diameter bolt
b b
Gusset plate
7/8 in. diameter bolt
b b
Gusset plate
7/8 in. diameter bolt
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aa
5 x in. bar
A572 Gr. 50
aa
5 x in. bar
aa
5 x in. bar
A572 Gr. 50
Net Area Ex ample
Gross section area (Ag):
A = 5 x = 2.5 in2g
Net section area (An):
Bolt diameter = db = 7/8 in.
Nominal hole diameter = dh
= 7/8 + 1/16 in. = 15/16 in.
Hole diameter for calculatin net area = 15/16 + 1/16 in. = 1 in.
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Net section area = An
= (5 2 x (1)) x = 1.5 in2
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Net Area Ex ample
Gross yielding design strength:
t n=
t yAg
= 0.9 x 50 ksi x 2.5 in2 = 112.5 kips
Fracture design strength:
ftPn = ft Fu Ae= 0.75 x 65 ksi x 1.5 in2 = 73.125 kips
Assume Ae
= An
(only for this problem)
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Therefore, design strength = 73.125 kips (net section fracture
controls).
Shear Lag i n Tension
Members Shear lag in tension members arises when all theelements of a cross section do not artici ate in theload transfer at a connection.There are two primary phenomena that arise inthese cases:
(i) Non-uniform straining of the web resulting in
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ax a s ress s a es(ii) Effective area reduction.
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Shear Lag i n Tension
Members
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Shear Lag i n Tension
MembersEffective area reduction
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Shear Lag i n Tension
MembersDesign Bottom Line
Shear lag can have a large influence on the
strength of tension members , in essence
reducing the effective area of the section. The
amount of the reduction is related to the length of
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section elements that do not participate directly in
the connection load transfer.
Bloc k Shear in Tension
Members
Block shear is a combined tensile/shear tearing
out of an entire section of a connection.
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Bloc k Shear in Tension
Members,
two possible mechanisms:
(1) Shear rupture + tensile yielding; and
(2) Shear yielding + tensile rupturing.
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Bloc k Shear in Tension
Members
As a likely limit state for connections,block shear must be considered indesign. This can be accomplished byconsiderin the stren th limit states of
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the two failure mechanisms outlinedabove.
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Design Ex am ple 1-ASD
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Desig n Ex am ple 1-LRFD
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Desig n Ex am ple 1-LRFD
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Design Ex am ple 2-ASD
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Design Alternative 2
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