Tension member

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INTRODUCTION

Department Of Civil Engineering

Govt. Poly. College,
Bathinda


Topic


Tension member

Subject


Steel Structures Design


Presenter
-

Er
.
Rani

Devi

B.E.(Civil), M.E. (Structures)

Mob.
-

9465265746


12th March, 2013

Punjab Edusat Society

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Introduction

Steel structures are structures in which the
members are made of steel and are joined by
welding, riveting, or bolting. Because of the high
strength of steel, these structures are reliable
and require less material than other types of
structures. In modern construction, steel
structures are widely used such as industrial
buildings, storage tankgas tanks, communication
structures (radio and television towers and
antennas), and power
-
engineering structures.


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The top beams in a truss are called top chords and
are generally in

compression, the bottom beams are
called bottom chords and are generally in

tension,
the interior beams are called webs, and the areas
inside the webs are called panels.

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Design for the steel frame of a twin
-
bay industrial building: (1) lattice, (2) column, (3)
crane girder, (4) skylight, and (5) web members

Tension Members

Members which are subjected to direct tension
are called tension members.


The Members can be of any standard steel
section
e.g.,

angle iron, channel section etc. In
case of frames and trusses, a tension member is
called a tie.

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Types of Sections

The types of section is governed by the nature and
magnitude of stresses to which, it is subjected. The
different type of sections are shown in figure and
classified as:


(1)
Rod, round or square :
-

These are used in
buildings for the lateral and sway bracings,
hangers, segmental arch floors and timber
trusses etc.

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(2) Flats :
-

These are used as tension member in
light trusses connected by welding at their
ends.


(3) Eye bars :
-

These are used in pin connected


Structures.


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(4) Single angle sections :
-

These are used as
tension member in light roof trusses, bracing
members in plate girder bridges and light
latticed girder bridges, not recommended as
best tension member as they are subjected to
bending stresses due to the eccentric loads.


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(5) Double angle section :
-

These are used
extensively in roof trusses, may be connected
to gusset plate on same or opposite faces i.e.,
by placing the gusset plate in between the
two angles. The later type of end connection
is preferred and more economical as it
eliminates bending stresses.




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(6) T
-
sections :
-

These are used as a substitute
of former type of double angles.


(7) Double channel section :
-

These are used for
heavy structures subjected to bending and
direct stresses.



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Strength of a Tension Member

The Strength of a Tie Member or load bearing
capacity of a tension member is calculated as :
-


Strength of a Tension Member =


Net area
×

Permissible tensile stress(
σ
at
).

The strength depends upon net area.

Permissible tensile stress(
σ
at
) for a tension
member is generally taken as 150MPa



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Net Sectional Area

Net sectional area of a tension member is the
gross cross section area of the member minus
the deduction for holes.

Case 1
-

For Plate :
In determining the net
sectional area of the plates, the arrangement of
the rivets plays an important role. The riveting in
plate can be of two types i.e.:

(a)Chain riveting

(b) Zig
-
Zag riveting.






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(a) Plates connected by Chain riveting :





Let, A
net

= Net cross sectional area along any


section 1
-
1


b = Width of Plate


n = number of rivets along the section
under consideration



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d = Gross diameter of the rivets


t = Thickness of the plate


A
net

= Gross area
-

area of plate lost in the
process of making holes


A
net

= b t
-

nd

t


A
net

= (b


nd
) t

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(b) Plates connected by Zig
-
Zag or staggered
riveting :





Let, A
net

= Net area of cross sectional


b = Width of Plate


n = number of rivets in the plane under
consideration.



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n’ = number of gauge distance


s = staggered pitch


g = gauge distance


t = Thickness of the plate




A
net
=




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Case 2
-

For single angle connected by one leg
only:




Net effective area,


i.e.,

A
net

= A
1

+ A
2
K


Where, A
net

= Net cross
-
sectional area


A
1

= Net cross
-
sectional area of


connected leg



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A
1

= (length of leg


½ t


nd)
×

t


A
2

= Gross cross
-
sectional area of


outstanding leg


A
2

= (length of leg


½ t) x t



K = constant =



A
net

= A
1

+ A
2
K




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Case 3. For a pair of angles place over a single
tee connected by only one leg of each angle to
the same side of the gusset plate :







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Net effective area,


i.e.,

A
net

= A
1

+ A
2
K




Where, A
net

= Net cross
-
sectional area


A
1

= Net cross
-
sectional area of


connected leg
(flange of the tee)


A
2

= Gross cross
-
sectional area of


outstanding leg
(web of the tee)




K = constant =





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A
1

= 2 (length of leg


½t


nd)
×

t



A
2

= 2 (length of leg


½ t)
×

t


In case of T section




A
1

= (b
f
-

2d )
×

t
f




A
2

= Gross area of web


= t
w

×

(overall depth(h)


t
f
)




Case 4. For double angles or a tee placed back to
back and connected to each side of the gusset
or side of a rolled section. :
-





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Deduction for rivet holes = number of rivets
×

gross diameter of one rivet
×

thickness of plate
i.e., = n
×

d
×

t

Net effective area, A
net

= Gross area


Deduction
for rivet holes


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Problem 1: A plate 240mm wide and 12mm
thick is connected by 20mm
φ

rivets as shown.
Calculate the strength of the tension plate.
Take
σ
at

= 150N/mm
2


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Numerical Problems

Solution: Nominal dia. of rivet (D) =20mm


Gross dia. of rivet hole (d) = 20 +1.5


= 21.5mm

Width of plat = 30 + 60 + 60+ 60 + 30 = 240mm


s = 50mm


g = 60mm

Considering the failure of the plate along section
line 1
-
2
-
3
-
4, we have;


A
net
1

= (b


nd) t


t = 12mm, n = 2, b = 240mm, d = 21.5mm


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A
net
1
= (240
-
2
×

21.5)
×

12 = 3564mm
2

Now for area along staggered line 1
-
2
-
5
-
3
-
6
-
7



A
net
2

=


Where b = 240mm


n = 4


d = 21.5mm


n’ = 3


t = 12mm

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A
net
2

= = 2073 mm
2



Minimum net area of section = A
net
2


Strength of the plate = 2073
×

150 = 310950


= 310.95kN


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Problem 2: Calculate the strength of a tie
composed of ISA 100
×

75
×

8mm with longer
legs connected by 16mm dia. rivets. Take
σ
at

=
150N/mm
2

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Solution: Nominal dia. of rivet = 16mm


Gross dia. of rivet = 16 + 1.5 = 17.5mm

Net Area; A
net
= A
1

+ A
2
K




A
1

= = 628mm
2



A
2
= 561mm
2



K= constant =





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A
net
= A
1

+ A
2
K


= 628 + 561
×

0.77 = 1059.97mm
2

Strength of ISA 100
×

75
×

8 = 1059.97mm
2
×

150


= 158995.5N


= 158.99kN

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Problem 3: Calculate the strength of a tie
member composed of 2 ISA 125
×

75
×

8mm
placed back to back connected by longer legs
by 20mm dia. rivets on same side of the gusset
plate. Take
σ
at

= 150N/mm
2

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Solution: Nominal dia. of rivet (D) =20mm


Gross dia. of rivet hole (d) = 20 +1.5


= 21.5mm


A
net
= A
1

+ A
2
K


A
1

= = 1592mm
2


A
2

= = 1136mm
2



K = constant =






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K =


Net effective area A
net
= A
1

+ A
2
K


= 1592 + 1136
×

0.875


= 2586mm
2

Strength of tie member = 2586
×

150 = 387900N



= 387.9kN



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×

Problem 4: Calculate the strength of a tie
member composed of 2ISA 125
×

75
×

8mm
placed back to back connected by longer legs
by 20mm dia rivets on both sides of the gusset
plate.


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Solution: From steel table,

gross area of ISA 125
×

75
×

8mm


= 15.38cm
2
= 1538mm
2

Net effective area =

Gross area


Deduction for rivet holes


A
net
= 2[1538


21.5
×

8] = 2732mm
2



Strength of tie member = 2732
×

150


= 109.8kN



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Problem 5: Determine the strength of ISHT 75
which is used as a tie member. It is connected
through its flange by means of 20mm diameter
rivets. Take
σ
at

= 150N/mm
2


Solution: Data Given:


Tie member consists of ISHT 75


Nominal dia. of rivet (D) =20mm


Gross dia. of rivet hole (d) = 20 +1.5


= 21.5mm




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Thickness of Flange,
t
w

= 8.4mm



Thickness of web,
t
f

= 9mm



Overall Height = 75mm



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Case under consideration : Tee (or 2ISA)
connected on same side of the gusset plate by
riveting:


A
net
= A
1

+ A
2
K





K = constant =


Properties of ISHT 75 (From steel cables)


Width of plate, b = 150mm




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Net Area of flange, A
1

= (width of flange

nd
)
×

t
f




= (150


2
×

21.5)
×

9


(Since, number of rivets(n) = 2)



= 963mm
2

Gross area of web, A
2

= (75
-

9)
×

8.4


(Since, Area = Length of web
×

t
w
)



= 554.4mm
2



K =



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Net cross sectional area, A
net
= A
1

+ A
2
K



= 963 + 554.4
×

0.897



= 1460.29mm
2

Tensile Strength of the T


section = A
net
×

σ
at




= 1460.29
×

150



= 219043.5N



= 219.04kN

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Design of Members Subjected to Axial
Tension

Step 1. Calculation of the required net area


The axial pull (
force)
to be transmitted by the
member and the allowable stress in axial
tension (

permissible tensile force i.e.

σ
at
) are
known for the steel with yield stress f
y.


Net sectional area required =

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i.e.
A
net

reqd. =


Step 2. Selection of suitable section

Try a suitable section, from steel tables having
sectional area about 20 to 40% greater (in case
of riveted joint) and 10% greater (
in case of
welded joint
) than the required net area.

In case the member selected is ISA, than select
unequal angle and connect longer leg with
gusset plate for getting more strength
i.e.
(
load
carrying capacity
)


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Step 3. Calculate the net sectional (effective)
area of the selected section
(As discussed
earlier)


Step 4. Check for net Sectional area


The net area calculated for trial section
(in step 3) should be slightly greater than the
required net area. If it is so then selected
section is OK. Other wise try some other
section.

i.e.
Net area of trial section > Net area required


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Step 5. Check for Slenderness ratio (
λ
).

Slenderness ratio, is the ratio of effective length
of member to the least radius of gyration.


i.e.
Slenderness ratio
λ

=


The value of radius of gyration (
r
min

) can be
obtained from steel tables.

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1.
A tension member in which a reversal of direct
stress due to load other than wind or seismic
forces would occur, shall not have a slenderness
ratio more than 180.


2.
A member normally acting as a tie in a roof
truss, but subject to possible reversal of stress
resulting from the action of wind or seismic
forces shall have slenderness ratio not greater
than 350.

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Step 6. Design of end connections

The end connections may be designed as a
riveted connection or welded connection.

(a)
For riveted connection

(i)
Select suitable size of rivet and determine
the rivet value (
i.e.
least of
P
b

and P
f
)

(ii)
Find the number of rivets by the relation ;



Number of rivets required =



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(iii) The arrangement of rivets should be made in
such a way that :



there is no eccentricity of loading.


The centre of gravity of the section coincides
with the C.G. of group of rivets.

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(b) For welded connections

(i)
Find the minimum and maximum size of fillet
weld and select the suitable size of weld (S)
and find the value of effective throat
thickness, t = 0.7 S

(ii)
Calculate the strength of weld/mm length by
the formula;


=
τ
vf

×

l
×

t


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Problems Based On Design of Tension
Member

Problem 1.Design a tension member subjected
to pull of 165
kN

using unequal angles placed
back to back with their longer legs connected
on both sides of gusset plate by 18mm
diameter rivets. Use PDSR (Power Driven
Shop Rivets). Take
σ
at

= 150N/mm
2

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Solution : Data given ;


Load (axial pull) = 165kN = 165
×

10
3
N

Nominal dia. of rivet, D = 18mm

Gross dia. of rivet, d = 18 + 1.5 = 19.5mm

For PDSR,


τ
vf

= 100 N/mm
2


σ
pf

= 300 N/mm
2


σ
at

= 150 N/mm
2




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Net area required = =



= 1100mm
2


Assuming the gross area to be about 25% greater
than the net area


Gross area = 1100
×

1.25 = 1375mm
2


from steel cable, try 2 ISA gross area equal to or
greater than 1375mm
2

Let us try an ISA 80
×

50
×

6 mm @ 57.9 N/m =


7.46cm
2

or 746mm
2





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Gross area for 2 ISA = 2
×

746 = 1492mm
2

Longer legs are connected to the gusset plate
(as shown in Figure)

Case under construction : Two ISA connected
back to back on the both sides of the gusset
plate ( i.e. CASE IV)



A
net

= Gross area
-

Deduction for holes

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2 ISA connected back to back (
with
longer leg
connected) on the both sides of gusset [late


A
net

= 1492


(2
×

19.5)
×

6


= 1258 > 1100mm
2

Hence, use 2 ISA 80
×

50
×

6 mm @ 57.9 N/m as
a tension member.


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Design of riveted end connections

Shearing strength of one rivet (
in double shear
)


= 2
×

τ
vf

×





= 2
×

100
×





= 59729.53 N ...(1)



Bearing Strength of one rivet =
σ
pf

×

d
×

t


= 300
×

19.5
×

6


= 35100 N …(2)

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Least of (1) and (2) is the Rivet Value (R.V.)


R.V. = 35100 N


Number of rivets required =



Arrangements of rivets is as shown in Figure.


Provide pitch = 3
×

18 = 54 = 60mm c/c


Edge distance = 2
×

18 = 36 = 40mm



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CONCLUSION


Tension

member
.


Various

sections

which

are

used

as

tension

members
.


Strength

of

tension

members
.


Different

formulas

to

calculate

net

effective

area

for

various

sections
.


Design

of

Tension

Members
.



Problems
.

Thanks




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