Shear Stresses & Bending Moment.pptx

8/20/2019 Shear Stresses & Bending Moment.pptx

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Shear Stresses &Bending Moment

A study of stresses on beams and bending moment dstresses

Tutor: Javaria ChiraghGC University – Btech(E


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Beam

•Beam is a bar carrying e"terna forcesincined to its a"is# Beams areconsidered straight and e"terna foa$ays considered as vertica oads#

•Types of beams:

Beams are cassi%ed the $ay tsuorted

• Simply Supported Beams


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Simply Supported Beams

• A simy suorted beam is suortedby a hinged suort at one end androer suort at other end#

Overhanging Beams

• An 'verhanging suorted beam is asosuorted by a hinged and roersuorts but have one or both endse"tending beyond suorts#Cantilever Beams• Cantiever beams are ony suorted at

ony one end#


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Types of Loads•

Point Loadoint oad is aso caed concentrated oad# )tacts over so sma ength of beam that it can beassumed to act at a oint#

•Distributed Load• )t is sread over su*cient ength of beam# )t

may be distributed over entire ength or over aoint of beam#

• +istributed oad is $,-.unit ength


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Moment(Moment of fore!:

2he turning e3ect of a force is 4no$n a

moment# )t is the roduct of the forcemutiied by the moment arm

M,01d

Moment "rm:

)t is erendicuar distance from the in


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Sign Conventions in Beam

•

hysicay $econsider the ositiveand negativemoments/ if the

e3ect of e"ternaforces tend to bendthe beam as sho$nin %gure#

Smieys 5uto

remembe


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Shear # Bending MomentDiagrams•

Shear $ore (S$! diagram 2he Shear 0orce (6! ottedagainst distance " Measuredfrom end of the beam

• Bending moment (BM!diagram Bending moment (BM!otted against distance "Measured from end of the beam

S0 diagram

BMdiagram

7oaddiagram


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Bending moment in Simplsupported beam (Point Lo

• 0irsty/ $e have to cacuatereactions at suorts and dra$0ree Body +iagram (0B+!#

• 2hen from eft to right/ $e $ima4e 8cuts8 before and after

each reaction.oad


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Cut 9 Cut :

;et$of

Baosa

SB

;ere are sti onyone reaction toconsider on eft ofthe cut#

Bending momentat the center of thebeam>


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Bending moment in Simplysupported beam (Distributeload!


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Bending moment in antilevebeam (Point load!

• -e do bending momentanaysis of cantiever beamsimiary#

• Bending moment isdo$n$ards according to ourconvention#

•

Moment,0orce 1 Momentarm

• M,@-1" (for moment at !

• M,@-1 (for moment at 5oint!


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Bending moment in antilevbeam (Distributed load!


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%elations bet&een load' Shear $ore and bemoment

•

eationshi bet$eendistributed oad and shearforce is>

• -, d0.d"

• -here 0 is shear force and- is aied oad#

• )t means that rate ofchange of shear force atany section reresents rateof oading at that section#

• eationshi bet$een distributed shear formoment is>

• 0,dM.d"

• -here M is bending moment and 0 is shea

• )t means that rate of change of bending m

reresents shear force at that oint

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Shear Stresses & Bending Moment.pptx