Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf ·...
Transcript of Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf ·...
![Page 1: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/1.jpg)
Structure Analysis IStructure Analysis IStructure Analysis IStructure Analysis IChapter Chapter 77Chapter Chapter 77
![Page 2: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/2.jpg)
Approximate Analysis of Statically Approximate Analysis of Statically Indeterminate Structures
![Page 3: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/3.jpg)
IntroductionIntroduction• Using approximate methods to analyse statically g pp y yindeterminate trusses and frames
• The methods are based on the way the structure deforms under the loadunder the load
• Trusses• Portal frames with trusses• Vertical loads on building frames• Lateral loads on building frames
– Portal method– Cantilever method
![Page 4: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/4.jpg)
Approximate AnalysisApproximate Analysis
• Statically determinate structure – the force equilibrium equation is sufficient to find the support reactions
• Approximate analysis – is to develop a simple model of the• Approximate analysis is to develop a simple model of the structure which is statically determinate to solve a statically indeterminate problemTh th d i b d th th t t d f d• The method is based on the way the structure deforms under loads
• Their accuracy in most cases compares favourably with more exact methods of analysis (the statically indeterminate analysis)
![Page 5: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/5.jpg)
D t i TDeterminacy ‐ Trusses
jrb 2=+ Statically determinateStatically determinateStatically determinateStatically determinate
jrb 2>+ Statically indeterminateStatically indeterminateStatically indeterminateStatically indeterminate
b – total number of bars
r total number of external support reactions
b – total number of bars
r total number of external support reactionsr – total number of external support reactions
j – total number of joints
r – total number of external support reactions
j – total number of joints
![Page 6: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/6.jpg)
TrussesTrussesReal Structure
b=b=1616 r=r=33 j=j=88b=b=1616, r=, r=33, j=, j=88b+rb+r = = 19 19 > > 22j=j=1616The truss is statically indeterminate toThe truss is statically indeterminate to the third degree
![Page 7: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/7.jpg)
TrussesTrussesApproximation Method
Assumption 1: If the diagonals are designed to be long and slender, it is assumed that diagonals can g gnot support any compressive force and all panel shear are resisted only by tensile diagonals.Assumption 2: If the diagonals are designed to be large rolled sections such as angles or channels, the are ass med to s pport both tensile andthey are assumed to support both tensile and compressive forces. Each diagonal is assumed to carry half the panel shearcarry half the panel shear.
![Page 8: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/8.jpg)
ExampleExample 11Example Example 11
![Page 9: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/9.jpg)
![Page 10: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/10.jpg)
ExampleExample 22Example Example 22
![Page 11: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/11.jpg)
![Page 12: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/12.jpg)
![Page 13: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/13.jpg)
![Page 14: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/14.jpg)
Vertical Loads on Building FramesVertical Loads on Building Frames
• Building frames often consist of girders that are rigidly connected to columns
If the columns are If the columns are extremely stiffextremely stiffextremely stiffextremely stiff
If the columns areIf the columns are extremely flexible
Average point between the ≈
g ptwo extremes = (0.21L+0)/2 0.1L
![Page 15: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/15.jpg)
Vertical Loads on Building FramesVertical Loads on Building Frames Average point between the two extremes = (0.21L+0)/2
0 1y 0.1L
![Page 16: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/16.jpg)
Building Frames – Vertical LoadsReal structure Approximation
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxqxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxqxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
qx
0.1L 0.1L 0.1L 0.1Lxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
qx
0.1L 0.1L 0.1L 0.1L
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxx
xxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxx
xxxxxxxx
xxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxx
xxxxxxxxxxxx
0.1L 0.1L 0.1L 0.1L
xxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxx
xxxxxxxxxxxx
0.1L 0.1L 0.1L 0.1L
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
L Lxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
L Lxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
L Lxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
L Lxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxx
1.There is zero moment (hinge) in the girder 0.1L from the left support2. There is zero moment (hinge) in the girder 0.1L from the right support3.The girder does not support an axial force.
![Page 17: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/17.jpg)
Example 3Example 3
![Page 18: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/18.jpg)
![Page 19: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/19.jpg)
Portal Frames – Lateral LoadsPortal frames are frequently used over the entrance of a bridge or in industrial buildings.Portals can be pin supported fixed supported or supported by partialPortals can be pin supported, fixed supported or supported by partial fixity
![Page 20: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/20.jpg)
Pin Supported Portal FramesPin‐Supported Portal Frames
![Page 21: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/21.jpg)
Pin‐Supported Portal FramesPin Supported Portal Frames
![Page 22: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/22.jpg)
Fixed‐Supported Portal FramesFixed Supported Portal Frames
![Page 23: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/23.jpg)
Fixed‐Supported Portal FramesFixed Supported Portal Frames
![Page 24: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/24.jpg)
Partial Fixed‐Supported Portal FramesPartial Fixed Supported Portal Frames
![Page 25: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/25.jpg)
Portal Frames – Lateral Loads
xxxxxxxxxxxxxxxx
Pxxxxxxxxxxxxxxxx
P
Real Structure ApproximationPin-supported
xxxxxxxxxxxxxxx
Pxxxxxxxxxxxxxxx
P A point of inflection is
assumed hinge
A point of inflection is located approximately at the girder’s midpointOne assumption
must be madexxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
fixed -supportedxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxx
Pxxxxxxxxxxxxxxxx
Pxxxxxxxxxxxxxxx
Pxxxxxxxxxxxxxxx
P Points of inflection are located
must be made
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
h/2
h/2
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
h/2
h/2assumed
hinge
are located approximately at the midpoints of all three membersThree assumption
must be made
Partial fixityxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxx
Pxxxxxxxxxxxxxxxx
Pxxxxxxxxxxxxxxx
Pxxxxxxxxxxxxxxx
P Points of inflection for columns are located approximately at h/3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
h/3xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
h/3
assumed hinge
pp yand the centre of the girder
![Page 26: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/26.jpg)
Frames with TrussesFrames with Trusses• When a portal frame is used to span large distance, a truss may be
used in place of the horizontal girderused in place of the horizontal girder• The suspended truss is assumed to be pin connected at its points
of attachment to the columns• Use the same assumptions as those used for simple portal framesUse the same assumptions as those used for simple portal frames
![Page 27: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/27.jpg)
Frames with TrussesR l t t A i tiReal structure Approximation
xxxxxxxxxxxxxxxx
Pxxxxxxxxxxxxxxxx
Pxxxxxxxxxxxxxxx
Pxxxxxxxxxxxxxxx
P
V VV V
pin supported columns pin connection truss-column the horizontal reactions (shear) are equal
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
V V
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
V V
xxxxxxxxxxxxxxx
Pxxxxxxxxxxxxxxx
Pxxxxxxxxxxxxxxx
Pxxxxxxxxxxxxxxx
P
horizontal reactions (shear) are equalxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
h
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
h
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
h/2
h/2
V Vxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
h/2
h/2
V V
fixed supported columnspin connection truss-column
horizontal reactions (shear) are equalthere is a zero moment (hinge) on each column
![Page 28: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/28.jpg)
ExampleExample 44Example Example 44
![Page 29: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/29.jpg)
![Page 30: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/30.jpg)
![Page 31: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/31.jpg)
Building frames – Lateral Loads l h dPortal Method
• A building bent deflects in the same way as a portal frameframe
• The assumptions would be the same as those used for portal framesportal frames
• The interior columns would represent the effect of two pportal columns
![Page 32: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/32.jpg)
Building frames – Lateral loads Portal MethodPortal Method
real structure approximation
xxxxxxxxxxxxxxxx
Pxxxxxxxxxxxxxxxx
P
xxxxxxxxxxxxxxxx
P
V1 2V1 V1
xxxxxxxxxxxxxxxx
P
V1 2V1 V1
2VV V2VV V
1. A hinge is placed at the centre of each girder, f
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
The method is most suitable for buildings having low elevation and
this is assumed to be a point of zero moment.2. A hinge is placed at the centre of each
column, this to be a point of zero moment.3 At the given floor level the shear at theuniform framing 3. At the given floor level the shear at the
interior column hinges is twice that at the exterior column hinges
![Page 33: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/33.jpg)
Example 5Example 5
![Page 34: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/34.jpg)
![Page 35: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/35.jpg)
![Page 36: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/36.jpg)
Example 6Determine (approximately) the reactions at h b f h l f h f
Example 6
the base of the columns of the frame.
![Page 37: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/37.jpg)
![Page 38: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/38.jpg)
![Page 39: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/39.jpg)
Building frames – Lateral loads C il h dCantilever method
• The method is based on the same action as a long cantilevered beam subjected to a transverse loadbeam subjected to a transverse load
• It is reasonable to assume the axial stress has a linear variation from the centroid of the column areas
![Page 40: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/40.jpg)
Building frames – lateral loads: Cantilever methodCantilever method
Real structure Approximation
P xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxx
P
A B CNA=σA AA NB=σB AB NC=σC AC
xxxxxxx
xxxxxxx
xxxxxxx
xxxxxx
xxxxxxxxxxxxxxxx
Pxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
xxxxxx
xxxxx
xxxxxx
XT = (ΣXi Ai)/A
The method is most suitable if the frame is tall and slender, or has
1. Zero moment (hinge) at the centre of each girder2. Zero moment (hinge) at the centre of each column3. The axial stress in a column is proportional to its ,
columns with different cross sectional areas.
p pdistance from the centroid of the cross-sectional areas of the columns at a given floor level
![Page 41: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/41.jpg)
ExampleExample 77Example Example 77
![Page 42: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/42.jpg)
![Page 43: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/43.jpg)
![Page 44: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/44.jpg)
![Page 45: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/45.jpg)
ExampleExample 88Example Example 88
![Page 46: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/46.jpg)
![Page 47: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/47.jpg)
![Page 48: Structure Analysis I - site.iugaza.edu.pssite.iugaza.edu.ps/marafa/files/2010/02/Chapter_7.pdf · Introduction • Using approximate methods to analysestatically ... structure which](https://reader031.fdocuments.us/reader031/viewer/2022021418/5aa881827f8b9a81188ba2fb/html5/thumbnails/48.jpg)