ENG1001 Lecture 3: Week 3 Trusses
30 May 2018
School
Department
Course
Professor
Made%up%of%triangles
More%stable%than%rectangular%elements
○
•
Used%to%stabilise%structures%against%horizontal%loads
•
Efficient%structural%forms%for%long%spans%like%bridges
•
Domestic%timber%construction%-cost-effective%compared%to%timber%
beams,%allow%plumbing%services%to%pass%through%floor
•
Individual%members%of%truss%experience%axial%tension%or%compression
Mathematical*assumptions:
Trusses%are%loaded%and%supported%only%at%the%joints.
Usually%acceptable,%since%secondary%structure%usually%
designed%to%line%up%w/%truss%joints
a.
1.
All%joints%in%a%truss%are%pin joints.
Typically%in%practice,%joints%usually%semi-rigida.
But%acc%to%comp%analysis,%if%loaded%@%joints,%moments%and%
shear%forces%extremely%small%compared%to%internal%axial%forces
b.
2.
Stability*
Unstable%if:
Support%restraints%are%insufficient%
(external)
<%3%reactions
○
Reactions%all%parallel
○
Lines%of%reaction%forces%are%
concurrent
○
•
Member%number%and%arrangement%
is%insufficient%(geometric)
No.%&%arrangement%of%
members%are%such%that%truss%
can%change%shape under%any%
loading%w/o%any%indiv%
members%deforming
○
•
Determinacy
Determinate%if%support%reactions%and%ALL%member%forces%can%be%calculated%
using%only%eq%eqns%(for%2D)
Must%have%min%no.%of%support%rctns%and%members%to%ensure%stability•
Indeterminate:
More%rctns%and/or%membs%than%needed,%thus%eq%eqns%alone%not%
enough%to%solve%for%forces
•
Sometimes%m%+%r%<%2j%is%applicable%for%unstable%
structures.%
Rely%on%formula%for%determinacy,%NOT%STABLITY.
Internal*member*forces
All%stable%structures%have%internal%forces%in%eq.
To%find%values,%boundary%of%FBD%can%cut%through%a%member,%
exposing%the%internal%forces.
Forces%in%truss%members%are%ONLY%axial%
(tension/compression).
Members%sometimes%referred%to%as%'two-force%
members'
-
**Always%draw%unknown force%arrows away%from%the%joint
Indicates%tension
If%value%+ve,%tension%(T),%if%not,%compression%(C)
(to*find*internal*memb*forces*of*trusses)
Method*of*joints*
Analyse%a%'determinate'%truss%by%creating%a%FBD%at%each%joint
**forces%are%concurrent!
Start%%at%a%joint%with%only%2%unknowns1.
Work%through%structure%one%joint%at%a%time%utilising%prev%calced%
values
2.
**Resolve%angled%forces%using%horizontal%cosine%component%and%vertical%
sine%component.%(45d)
Don't%take%these%into%account%when%calculating%moment%sum!
**Take%moments%where%2%of%the%unknown%forces%meet/are%concurrent.
**Check%if%T%or%C%is%right%for%each%member%by%visualising%load
**for%simple%single%layer%trusses%w/%a%pin%and%roller% support%only,%truss%
must%be%triangulated%to%be%stable.
(to*find*internal*memb*forces*of*trusses)
Method*of*sections
**forces%not%(all)%concurrent!
No%need%to%rely%on%prev%calced%values.
Use%eq%to%find%support%reactions
**making%use%of%symmetry%is%possible!
1.
Cut%through%truss%@%members%(pref%halfway)%and%create%FBD%either%
side%of%the%cut
Assume%all%unknowns%are%tension%as%usual%(+ve%T,%-ve%C)
3%unknowns,%not%2
Unknown%forces%don't%converge,%so%sum%of%moments%eqn%can%be%
applied.
2.
Preferable%to%take%moments%abt%2%points%to%find%unknown%forces,%since%no%
need%to%rely%on%prev%calced%values.
Week$3:$Trusses
Friday,%4%August%2017
12:17
Made%up%of%triangles
More%stable%than%rectangular%elements
○
•
Used%to%stabilise%structures%against%horizontal%loads•
Efficient%structural%forms%for%long%spans%like%bridges•
Domestic%timber%construction%-cost-effective%compared%to%timber%
beams,%allow%plumbing%services%to%pass%through%floor
•
Individual%members%of%truss%experience%axial%tension%or%compression
Mathematical*assumptions:
Trusses%are%loaded%and%supported%only%at%the%joints.
Usually%acceptable,%since%secondary%structure%usually%
designed%to%line%up%w/%truss%joints
a.
1.
All%joints%in%a%truss%are%pin joints.
Typically%in%practice,%joints%usually%semi-rigid
a.
But%acc%to%comp%analysis,%if%loaded%@%joints,%moments%and%
shear%forces%extremely%small%compared%to%internal%axial%forces
b.
2.
Stability*
Unstable%if:
Support%restraints%are%insufficient%
(external)
<%3%reactions
○
Reactions%all%parallel
○
Lines%of%reaction%forces%are%
concurrent
○
•
Member%number%and%arrangement%
is%insufficient%(geometric)
No.%&%arrangement%of%
members%are%such%that%truss%
can%change%shape under%any%
loading%w/o%any%indiv%
members%deforming
○
•
Determinacy
Determinate%if%support%reactions%and%ALL%member%forces%can%be%calculated%
using%only%eq%eqns%(for%2D)
Must%have%min%no.%of%support%rctns%and%members%to%ensure%stability
•
Indeterminate:
More%rctns%and/or%membs%than%needed,%thus%eq%eqns%alone%not%
enough%to%solve%for%forces
•
Sometimes%m%+%r%<%2j%is%applicable%for%unstable%
structures.%
Rely%on%formula%for%determinacy,%NOT%STABLITY.
Internal*member*forces
All%stable%structures%have%internal%forces%in%eq.
To%find%values,%boundary%of%FBD%can%cut%through%a%member,%
exposing%the%internal%forces.
Forces%in%truss%members%are%ONLY%axial%
(tension/compression).
Members%sometimes%referred%to%as%'two-force%
members'
-
**Always%draw%unknown force%arrows away%from%the%joint
Indicates%tension
If%value%+ve,%tension%(T),%if%not,%compression%(C)
(to*find*internal*memb*forces*of*trusses)
Method*of*joints*
Analyse%a%'determinate'%truss%by%creating%a%FBD%at%each%joint
**forces%are%concurrent!
Start%%at%a%joint%with%only%2%unknowns1.
Work%through%structure%one%joint%at%a%time%utilising%prev%calced%
values
2.
**Resolve%angled%forces%using%horizontal%cosine%component%and%vertical%
sine%component.%(45d)
Don't%take%these%into%account%when%calculating%moment%sum!
**Take%moments%where%2%of%the%unknown%forces%meet/are%concurrent.
**Check%if%T%or%C%is%right%for%each%member%by%visualising%load
**for%simple%single%layer%trusses%w/%a%pin%and%roller% support%only,%truss%
must%be%triangulated%to%be%stable.
(to*find*internal*memb*forces*of*trusses)
Method*of*sections
**forces%not%(all)%concurrent!
No%need%to%rely%on%prev%calced%values.
Use%eq%to%find%support%reactions
**making%use%of%symmetry%is%possible!
1.
Cut%through%truss%@%members%(pref%halfway)%and%create%FBD%either%
side%of%the%cut
Assume%all%unknowns%are%tension%as%usual%(+ve%T,%-ve%C)
3%unknowns,%not%2
Unknown%forces%don't%converge,%so%sum%of%moments%eqn%can%be%
applied.
2.
Preferable%to%take%moments%abt%2%points%to%find%unknown%forces,%since%no%
need%to%rely%on%prev%calced%values.
Week$3:$Trusses
Friday,%4%August%2017 12:17
Document Summary
Efficient structural forms for long spans like bridges. Domestic timber construction - cost-effective compared to timber beams, allow plumbing services to pass through floor. Individual members of truss experience axial tension or compression. Trusses are loaded and supported only at the joints. a. Usually acceptable, since secondary structure usually designed to line up w/ truss joints designed to line up w/ truss joints. All joints in a truss are pin joints. a. b. But acc to comp analysis, if loaded @ joints, moments and shear forces extremely small compared to internal axial forces. & arrangement of members are such that truss can change shape under any loading w/o any indiv members deforming. Determinate if support reactions and all member forces can be calculated using only eq eqns (for 2d) Must have min no. of support rctns and members to ensure stability. More rctns and/or membs than needed, thus eq eqns alone not enough to solve for forces.
