ENG1001 Lecture Notes - Lecture 6: Bending Moment
30 May 2018
School
Department
Course
Professor
Load%carried%by:%bending/shear
Bending moment%=%internal%action%which%curves a%beam%(one%side%of%
beam%shortens,%other%stretches)
•
Shear force%=%internal%action%trying%to%slide%one%part%of%a%solid%over%
another%>>>%distortion
•
Very%important%>>>%make%up%bending%(more%critical%for%design) and%shear%
stresses%which%develop%in%a%beam
•
Stress Axial0(normal) Bending
Applied%axial%force%spreads%quickly%
through%member%cross-section,%
forming%an%'internal'%uniform
stress%profile.
Either%tensile%(stretched)%%or%
compressive%(squashed).
'Internal'%stress%profile%no%longer%
uniform%but%triangular!
Tension%one%face,%compression%
the%other
Beams%best%made%from%materials%that%can%transfer%BOTH%tensile%and%
compressive%stresses%(eg.%steel,%timber,%reinforced%concrete)
•
Axial%force%(H)%=%sum%of%x-forces
If%0,%that%means%no%external%horizontal%forces%acting%on%
beam.
Shear%force%(V)%=%sum%of%y-forces
Bending%moment%(M)%=%sum%of%moments
Calculating0shear0force
'Cutting%a%distance%'x'% from%the%left%yields%the%FBD%
SFD
=%a%plot%of%the%cumulative%vertical%forces%as%a%function%of%the%distance%
along%the%beam
Horizontal%except%where%load%is%applied•
Point%load =%sudden%drop%in%the%shear•
UDL =%linear%reduction%in%the%shear•
Must return%to%zero when%the%end%of%beam%is%reached•
Calculating0bending0moment
BMD
(since%the%bridge%is%sagging)
Graphical0method0to0determine0BFD
Week$6:$Beams
Friday,%25%August%2017
13:42
Load%carried%by:%bending/shear
Bending moment%=%internal%action%which%curves a%beam%(one%side%of%
beam%shortens,%other%stretches)
•
Shear force%=%internal%action%trying%to%slide%one%part%of%a%solid%over%
another%>>>%distortion
•
Very%important%>>>%make%up%bending%(more%critical%for%design) and%shear%
stresses%which%develop%in%a%beam
•
Stress
Axial0(normal)
Bending
Applied%axial%force%spreads%quickly%
through%member%cross-section,%
forming%an%'internal'%uniform
stress%profile.
Either%tensile%(stretched)%%or%
compressive%(squashed).
'Internal'%stress%profile%no%longer%
uniform%but%triangular!
Tension%one%face,%compression%
the%other
Beams%best%made%from%materials%that%can%transfer%BOTH%tensile%and%
compressive%stresses%(eg.%steel,%timber,%reinforced%concrete)
•
Axial%force%(H)%=%sum%of%x-forces
If%0,%that%means%no%external%horizontal%forces%acting%on%
beam.
Shear%force%(V)%=%sum%of%y-forces
Bending%moment%(M)%=%sum%of%moments
Calculating0shear0force
'Cutting%a%distance%'x'% from%the%left%yields%the%FBD%
SFD
=%a%plot%of%the%cumulative%vertical%forces%as%a%function%of%the%distance%
along%the%beam
Horizontal%except%where%load%is%applied•
Point%load =%sudden%drop%in%the%shear•
UDL =%linear%reduction%in%the%shear•
Must return%to%zero when%the%end%of%beam%is%reached•
Calculating0bending0moment
BMD
(since%the%bridge%is%sagging)
Graphical0method0to0determine0BFD
Week$6:$Beams
Friday,%25%August%2017 13:42
Load%carried%by:%bending/shear
Bending moment%=%internal%action%which%curves a%beam%(one%side%of%
beam%shortens,%other%stretches)
•
Shear force%=%internal%action%trying%to%slide%one%part%of%a%solid%over%
another%>>>%distortion
•
Very%important%>>>%make%up%bending%(more%critical%for%design) and%shear%
stresses%which%develop%in%a%beam
•
Stress Axial0(normal) Bending
Applied%axial%force%spreads%quickly%
through%member%cross-section,%
forming%an%'internal'%uniform
stress%profile.
Either%tensile%(stretched)%%or%
compressive%(squashed).
'Internal'%stress%profile%no%longer%
uniform%but%triangular!
Tension%one%face,%compression%
the%other
Beams%best%made%from%materials%that%can%transfer%BOTH%tensile%and%
compressive%stresses%(eg.%steel,%timber,%reinforced%concrete)
•
Axial%force%(H)%=%sum%of%x-forces
If%0,%that%means%no%external%horizontal%forces%acting%on%
beam.
Shear%force%(V)%=%sum%of%y-forces
Bending%moment%(M)%=%sum%of%moments
Calculating0shear0force
'Cutting%a%distance%'x'% from%the%left%yields%the%FBD%
SFD
=%a%plot%of%the%cumulative%vertical%forces%as%a%function%of%the%distance%
along%the%beam
Horizontal%except%where%load%is%applied
•
Point%load =%sudden%drop%in%the%shear
•
UDL =%linear%reduction%in%the%shear
•
Must return%to%zero when%the%end%of%beam%is%reached
•
Calculating0bending0moment
BMD
(since%the%bridge%is%sagging)
Graphical0method0to0determine0BFD
Week$6:$Beams
Friday,%25%August%2017 13:42
Document Summary
Bending moment = internal action which curves a beam (one side of beam shortens, other stretches) Shear force = internal action trying to slide one part of a solid over another >>> distortion. Very important >>> make up bending (more critical for design) and shear stresses which develop in a beam. Applied axial force spreads quickly through member cross-section, forming an "internal" uniform stress profile. "internal" stress profile no longer uniform but triangular! Beams best made from materials that can transfer both tensile and compressive stresses (eg. steel, timber, reinforced concrete) "cutting a distance "x" from the left yields the fbd. = a plot of the cumulative vertical forces as a function of the distance along the beam. Point load = sudden drop in the shear. Must return to zero when the end of beam is reached. If 0, that means no external horizontal forces acting on beam.
