lecture -06 tension members_for print

8/8/2019 Lecture -06 Tension Members_for Print

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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

[email protected]

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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Sec t ions for Tension Members



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Sec t ions for Tension Members


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


, .


b b

Gusset plate

7/8 in . diameter hole

Section b-bb b

Gusset plate


b b

Gusset plate


Section b-bSection b-b


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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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


aa

8 x in. bar


Section a-aSection a-a


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.


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.


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


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


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.



Joint efficiency is a function of:

(a) Material ductility

(b) Fastener spacing

(c) Stress concentration at holes

(d) Fabrication procedure


(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


For bolted connection, t e effective net area is Ae = UAn

For welded connection, the effective net area is Ae = UAg


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


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


b b

Gusset plate



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.


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)


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


ax a s ress s a es(ii) Effective area reduction.


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Members



MembersEffective area reduction



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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


-

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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Members,

two possible mechanisms:

(1) Shear rupture + tensile yielding; and

(2) Shear yielding + tensile rupturing.



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


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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Design Alternative 2




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lecture -06 tension members_for print

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