Lecture 2 Bearing and Punching Stress, Strain

8/11/2019 Lecture 2 Bearing and Punching Stress, Strain

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Engineering Science (ES) 13:Mechanics of Deformable Bodies

Lecture 2:Bearing Stress

Punching Stress

Normal StrainShear Strain

1stSem AY 2014-2015

August 15, 2014


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Bearing Stress

Special type of axial stress

Commonly seen in:

connections (pins, bolts, rivets)

base plates/bearing plates of columns


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Average Bearing Stress

Connections

=

Bearing Plates

=

=

NOTE: stress distribution is complicated

so bis an average nominal value


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Example: Bearing Stress in

Connections

What is the bearing

stress between pin C

and member ABC?

What is the bearing stress

between pin C and the

links connecting BC?


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Example: Bearing Plate

A 40-kN axial load is applied to a short woodenpost that is supported by a concrete footing resting

on undisturbed soil. Determine (a) the bearing

stress on the concrete footing, (b) the size of the

footing for which the average bearing stress in thesoil is 145 kPa.


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Punching Stress

Special type of shear

stress

Experienced when:punching a hole on a

member

=


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Example: Punching Stress

A 20-mm thick metal plate with dimensions

150 mm by 120 mm is to be punched with a

12 mm diameter hole. The force P that will beused to punch the hole is estimated to be 40

kN. Determine the punching shear stress that

will be developed.


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STRAIN

describes the deformation of a body

change in length or angles
http://web.me.com/iaiachronicle/The_IAIA_CHRONICLE_Vol._8_Issue_3_May_2009/Iron_Beam_Bends_on_New_CLE_Building.html


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Normal Strain under Axial

Loading

L

L L

Deformation of a member per unit length

NOTE:

Deformation is always along the member

Strain is an average value and is constant

throughout the length of the member

where:

= axial strain

= deformation

L = length of

member

UNITS: mm/mm or m/m

SIGN: (+) elongates (-) shortens


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Shear StrainChange in angle between two originally

perpendicular segments

2

2

=

2

where:

- shear strain- new angle betweentwo lines initially

perpendicular lines

SIGN:

(+) when < /2(-) when > /2UNITS: radians


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Small Strain Analysis

For very small deformations:

where is in radians

sin

cos 1

tan


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Example: Normal Strain

A rigid bar AD is supported bytwo rods as shown. There is

no strain in the vertical bars

before load P is applied. After

load P is applied, the axialstrain in rod BF is -400 m/m.

Determine:

axial strain in rod CE.

axial strain in rod CE ifthere is a 0.25-mm

clearance in the connection

at pin C before the load is

applied.


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Example: Normal Strain

The load P produces an axialstrain in the brass post B of

-0.0014 mm/mm. Determine

a. The axial strain in the

aluminum alloy rod A.

b. The axial strain in the

aluminum alloy rod A if there

is a 0.125-mm clearance in

the connection between A

and C in addition to the 0.25-

mmclearance between B and

C.


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Example: Shear Strain

A thin rectangular plate isdeformed as shown. The

normal strains developed

along the sides are as

follows:AB= + 0.0022 mm/mm

BC= - 0.0030 mm/mm

CD= + 0.0050 mm/mm

Determine:

Horizontal displacement of B.

Normal strain in AD.

Shearing strain at A.

Shearing strain at C.


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Example: Normal + Shear

StrainThe counter-clockwise moment M applied to the rigidL-bar B produces an axial strain of -0.004444 mm/mm

in bar A and a shearing strain of 0.007 radians at E,

and causes support F to yield by 2 mm. Determine the

axial strain in bar C if there is a 0.5 mm clearance inthe connection between the triangular plate and the

rigid L-bar D.


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References

Beer, F.P. et al. (2006). Mechanics ofmaterials. 6thEd. SI. McGraw-Hill

Hibbeler, R.C. (2000). Mechanics of

materials. 4thEd. Prentice Hall

Lecture 2 Bearing and Punching Stress, Strain

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