ENG1001 Lecture Notes - Lecture 1: Space Frame
30 May 2018
School
Department
Course
Professor
!"#$%
="a"horizontal"member"supporting"vertical"loads
Most"common"structural"form
Beam"bends,"and"curves
1.
Tension"on"face"of"beam"stretching"&'#()
*"#+),-)'.#'/0(12,"compression"on"face"
squashing
2.
**Best"made"frm"materials"that"can"
transfer"both"tensile"and"compressive"
stresses"(eg.stone,"timber,"steel,"reinforced"
concrete)
304".,% loads
Creates"open"space"beneath"
Curves"(top"shorter,"bottom"longer)
5#6*"%)(>"beams)"(aka"funicular strucs)
="a"group"of"metallic"ropes"blended"tgt
Shape of"cable"changes with"load,"such"that"cable"must"always"carry"only"
tension
Only"works"in"#70#*),"(%0-(,"so"load"MUST"BE"IN"LINE"with"cable
Not"as"useful"but"still"efficient
Eg."suspension"bridge"-main"cable"supports"many"hanger"cables
Eg."cable-stayed"bridge"-cables"connect"directly"to"deck
8.'9"% (aka"opp"of"cable)
Carries"load"by"axial"compression
Vertical"loads"are"turned"into"radial"compression"forces,"which"are"then"reacted"
by"the"abutments
Can"never"be"as"slender"as"a"cable,"because
Arch"wants"to"6:'/*" due"to"compression
To"prevent"buckling,"needs"to"have"6"(+0(1)%,0;;("%%
Cannot"change"shape"to"suit"load,"like"cable
Supports"have"to"resist"9-.0<)= vert"forces
For"each"load,"only"-(")>#.,0':*#.)%9#>" of"arch"will"carry"that"load"by">:.")
'-$>."%%0-( in"the"arch">>>"most"efficient
Funicular"shape
Put"load"on"cable1.
See"what"shape"cable"takes"up"==>"pure"tension2.
Flip"shape"upside"down"to"get"arch"carrying"load"by"pure"compression3.
NOT"funicular"shape
Load"carried"by"'-$>."%%0-()?)6"(+0(1)$-$"(,
The"further"away"the"shape"frm"funicular"shape,"the"more"bending"moment"in"
arch
Beams
1.
Cables
2.
Arches
3.
Trusses
4.
3D"struc"forms
5.
@.:%%"%
="triangular"structures"efficient"for"large"spans,"where"all"inner"workings"are"
exposed
More"stable"than"rectangular"arrangement
Comprises"structural"members"arranged"in"a"triangular"fashion"w/"pin-jointed"
connections/'nodes'
A#'9)0(+04)$"$6 carries"its"load"by"axial" tension/compression
Get"%9-.,".B*-(1".)C0,9)(-)':.40(1,"but"truss"curves"#%)#)C9-*"D)*0/")#)
6"#$
304".,% loads
Creates"open"space"beneath
Curves"like"a"beam"(top"compressed,"bottom"in"tension)
E3
="when"a"load"is"dispersed"along"load"paths"existing"in"all"3"dimens
vs"2D:"easier"to"dev"math"models"of"real"strucs,
because"2D"forms"can"be"treated"as"a"series"of"repeated"2D"strucs"joined"tgt"
to"form"a"3D"struc
F*#6%)#(+)G*#,"%
="3D"beam,"bends"in"2"directns"@"same"time
H",%B$"$6.#("%
="3D"cable
E3)-;I
Beam
F*#6%)=)
>*#,"%
Bending"and"
shear
Bends"in"2"dirs"@"same"time
Cable
H",B
J"$6.#("
Axial"tension
Cables"kept"discrete">>>"net"
Cables"merge"to"form"
continuum">>>"membrane
**can"cover"large"areas"w/"light"
structures"bcos"of"efficiency"(pure"
tension"to"carry"load)
Arch
F9"**B+-$"
Axial"
compression
Provide"many"alt"paths"for"any"
applied"load
Thinner,"eleganter"strucs"possible"
w/"3D"than"2D,"because"load"paths"
can"be"dispersed"through"struc
Truss
F>#'");.#$"
Axial"
tension/
compression
Can"span"large"dist,"because"load"
dispersed"though"many"load"paths
K-*+"+)>*#," **illustrates"imptance"of"shape"in"
determining"strength"and"stiffness"
of"a"struc"form
="a"flat"sheet"folded"into"a"series"
of"peaks"and"valleys"
>>>"stiffer"and"stronger!
(eg."long"span"concrete"roofs)
Week$1:$Structural$Forms
Saturday,"22"July"2017
15:05
!"#$%
="a"horizontal"member"supporting"vertical"loads
Most"common"structural"form
Beam"bends,"and"curves1.
Tension"on"face"of"beam"stretching"&'#()
*"#+),-)'.#'/0(12,"compression"on"face"
squashing
2.
**Best"made"frm"materials"that"can"
transfer"both"tensile"and"compressive"
stresses"(eg.stone,"timber,"steel,"reinforced"
concrete)
304".,% loads
Creates"open"space"beneath"
Curves"(top"shorter,"bottom"longer)
5#6*"%)(>"beams)"(aka"funicular strucs)
="a"group"of"metallic"ropes"blended"tgt
Shape of"cable"changes with"load,"such"that"cable"must"always"carry"only"
tension
Only"works"in"#70#*),"(%0-(,"so"load"MUST"BE"IN"LINE"with"cable
Not"as"useful"but"still"efficient
Eg."suspension"bridge"-main"cable"supports"many"hanger"cables
Eg."cable-stayed"bridge"-cables"connect"directly"to"deck
8.'9"% (aka"opp"of"cable)
Carries"load"by"axial"compression
Vertical"loads"are"turned"into"radial"compression"forces,"which"are"then"reacted"
by"the"abutments
Can"never"be"as"slender"as"a"cable,"because
Arch"wants"to"6:'/*" due"to"compression
To"prevent"buckling,"needs"to"have"6"(+0(1)%,0;;("%%
Cannot"change"shape"to"suit"load,"like"cable
Supports"have"to"resist"9-.0<)= vert"forces
For"each"load,"only"-(")>#.,0':*#.)%9#>" of"arch"will"carry"that"load"by">:.")
'-$>."%%0-( in"the"arch">>>"most"efficient
Funicular"shape
Put"load"on"cable1.
See"what"shape"cable"takes"up"==>"pure"tension2.
Flip"shape"upside"down"to"get"arch"carrying"load"by"pure"compression3.
NOT"funicular"shape
Load"carried"by"'-$>."%%0-()?)6"(+0(1)$-$"(,
The"further"away"the"shape"frm"funicular"shape,"the"more"bending"moment"in"
arch
Beams1.
Cables2.
Arches3.
Trusses4.
3D"struc"forms5.
@.:%%"%
="triangular"structures"efficient"for"large"spans,"where"all"inner"workings"are"
exposed
More"stable"than"rectangular"arrangement
Comprises"structural"members"arranged"in"a"triangular"fashion"w/"pin-jointed"
connections/'nodes'
A#'9)0(+04)$"$6 carries"its"load"by"axial" tension/compression
Get"%9-.,".B*-(1".)C0,9)(-)':.40(1,"but"truss"curves"#%)#)C9-*"D)*0/")#)
6"#$
304".,% loads
Creates"open"space"beneath
Curves"like"a"beam"(top"compressed,"bottom"in"tension)
E3
="when"a"load"is"dispersed"along"load"paths"existing"in"all"3"dimens
vs"2D:"easier"to"dev"math"models"of"real"strucs,
because"2D"forms"can"be"treated"as"a"series"of"repeated"2D"strucs"joined"tgt"
to"form"a"3D"struc
F*#6%)#(+)G*#,"%
="3D"beam,"bends"in"2"directns"@"same"time
H",%B$"$6.#("%
="3D"cable
E3)-;I
Beam
F*#6%)=)
>*#,"%
Bending"and"
shear
Bends"in"2"dirs"@"same"time
Cable
H",B
J"$6.#("
Axial"tension
Cables"kept"discrete">>>"net"
Cables"merge"to"form"
continuum">>>"membrane
**can"cover"large"areas"w/"light"
structures"bcos"of"efficiency"(pure"
tension"to"carry"load)
Arch
F9"**B+-$"
Axial"
compression
Provide"many"alt"paths"for"any"
applied"load
Thinner,"eleganter"strucs"possible"
w/"3D"than"2D,"because"load"paths"
can"be"dispersed"through"struc
Truss
F>#'");.#$"
Axial"
tension/
compression
Can"span"large"dist,"because"load"
dispersed"though"many"load"paths
K-*+"+)>*#," **illustrates"imptance"of"shape"in"
determining"strength"and"stiffness"
of"a"struc"form
="a"flat"sheet"folded"into"a"series"
of"peaks"and"valleys"
>>>"stiffer"and"stronger!
(eg."long"span"concrete"roofs)
Week$1:$Structural$Forms
Saturday,"22"July"2017 15:05
Document Summary
Tension on face of beam stretching (can lead to cracking), compression on face squashing. **best made frm materials that can transfer both tensile and compressive stresses (eg. stone, timber, steel, reinforced concrete) = a group of metallic ropes blended tgt. Shape of cable changes with load, such that cable must always carry only tension. Only works in axial tension, so load must be in line with cable. Eg. suspension bridge - main cable supports many hanger cables. Eg. cable-stayed bridge - cables connect directly to deck. = triangular structures efficient for large spans, where all inner workings are exposed. Comprises structural members arranged in a triangular fashion w/ pin-jointed connections/"nodes" Each indiv memb carries its load by axial tension/compression. Get shorter/longer with no curving, but truss curves as a whole, like a beam. Curves like a beam (top compressed, bottom in tension) Vertical loads are turned into radial compression forces, which are then reacted by the abutments by the abutments.
