SlideShare a Scribd company logo
1 Prepared by Prof. Shehab Mourad – Department of Civil Eng. - KSU
Effective Length of Columns
The effective column length (the equivalent half wave of buckling
length), depends on;
1) The fixed end conditions (fixed, hinged or free ends), of the column
(K factor).
2) The framing condition, whether it is braced or unbraced
L L
Braced Frame
(Sway prevented) Unbraced Frame
(Sway Permitted)
P P P P
0.5 < K< 1.0 1.0 < K 5.0
K≤ 1 K≥ 2
Ib
2 Prepared by Prof. Shehab Mourad – Department of Civil Eng. - KSU
3) The column - beam connections, and the relative stiffnesses of columns
to beams at each end of the column
S (I/L) columns
G =
S (I/L) beams
Note : G = 10 for hinged (pinned) support
G = 1.0 for fixed support
For braced Frame
Km = 3 Gi Gj + 1.4 (Gi + Gj) + 0.64
3 Gi Gj + 2 (Gi+Gj) + 1.28
For unbraced Frame
Km = 1.6 Gi Gj + 4 (Gi+Gj) + 7.5
Gi + G j + 7.5
Or by using charts:
3 Prepared by Prof. Shehab Mourad – Department of Civil Eng. - KSU
Example
For the shown two storey frame with the indicated relative
Inertias, computed the Buckling length factor (K) for columns 1, 2 and 3.
Solution:
G1= 10 for hinged support
G3 = G6 = 1.0 for fixed support
G2 = (I/5) = 0.60
(2I /6)
G4 = ( 2I/5 + I/3 ) = 1.257
(2I/6 + 2I/8)
G5 = (I/3) = 1.332
(2I/8)
For Column 1, (unbraced frame) Values from charts
K1 = 1.6 x 10 x 0.6 + 4 (10 +0.6) + 7.5 = 1.81 1.80
10 + 0.60 + 7.5
For Column 2, (unbraced frame)
K2 = 1.6 x 1 x 1.257 + 4 (1 + 1.257) + 7.5 = 1.378 1.375
1 + 1.257 + 7.5
For Column 3, (braced Frame)
K3 = ( 3 x 1.257x1.332) + 1.4 (1.257 + 1.332) + 0.64 = 0.81 0.80
3 x 1.257 x 1.332 + 2 ( 1.257 + 1.332) + 1.28
5 m
3m
6m 8m
1
2
3
4
5
6
7
8
I 2I
2I 2I
2I
I I
I1 2
3

More Related Content

What's hot

ACI 318-19 Ingles.pdf
ACI 318-19 Ingles.pdfACI 318-19 Ingles.pdf
ACI 318-19 Ingles.pdf
fjimmy
 
89505650 concrete-beam-and-slab-design-using-prokon
89505650 concrete-beam-and-slab-design-using-prokon89505650 concrete-beam-and-slab-design-using-prokon
89505650 concrete-beam-and-slab-design-using-prokon
OscarKonzult
 
ETABS manual - Seismic design of steel buildings according to Eurocode 3 & 8
ETABS manual - Seismic design of steel buildings according to Eurocode 3 & 8 ETABS manual - Seismic design of steel buildings according to Eurocode 3 & 8
ETABS manual - Seismic design of steel buildings according to Eurocode 3 & 8
Eur Ing Valentinos Neophytou BEng (Hons), MSc, CEng MICE
 
19-Examples for Beam Column (Steel Structural Design & Prof. Shehab Mourad)
19-Examples for Beam Column (Steel Structural Design & Prof. Shehab Mourad)19-Examples for Beam Column (Steel Structural Design & Prof. Shehab Mourad)
19-Examples for Beam Column (Steel Structural Design & Prof. Shehab Mourad)
Hossam Shafiq II
 
37467305 torsion-design-of-beam
37467305 torsion-design-of-beam37467305 torsion-design-of-beam
37467305 torsion-design-of-beam
Sopheak Thap
 
Design of isolated footing by ACI code
Design of isolated footing by ACI codeDesign of isolated footing by ACI code
Design of isolated footing by ACI code
Mahmoud Al-Sharawi
 
Concrete shear wall design
Concrete shear wall designConcrete shear wall design
Concrete shear wall design
aj aj
 
23-Design of Column Base Plates (Steel Structural Design & Prof. Shehab Mourad)
23-Design of Column Base Plates (Steel Structural Design & Prof. Shehab Mourad)23-Design of Column Base Plates (Steel Structural Design & Prof. Shehab Mourad)
23-Design of Column Base Plates (Steel Structural Design & Prof. Shehab Mourad)
Hossam Shafiq II
 
Design of columns biaxial bending as per IS 456-2000
Design of columns  biaxial bending as per IS 456-2000Design of columns  biaxial bending as per IS 456-2000
Design of columns biaxial bending as per IS 456-2000
PraveenKumar Shanmugam
 
Etabs concrete-design
Etabs concrete-designEtabs concrete-design
Etabs concrete-design
mamilli
 
CE 72.52 - Lecture 7 - Strut and Tie Models
CE 72.52 - Lecture 7 - Strut and Tie ModelsCE 72.52 - Lecture 7 - Strut and Tie Models
CE 72.52 - Lecture 7 - Strut and Tie Models
Fawad Najam
 
06-Strength of Double Angle Welded Tension Members (Steel Structural Design &...
06-Strength of Double Angle Welded Tension Members (Steel Structural Design &...06-Strength of Double Angle Welded Tension Members (Steel Structural Design &...
06-Strength of Double Angle Welded Tension Members (Steel Structural Design &...
Hossam Shafiq II
 
6. safe users-guide
6.  safe users-guide6.  safe users-guide
6. safe users-guide
ALAN QUISPE CORONEL
 
Civil structural engineering - Flat slab design
Civil structural engineering -  Flat slab designCivil structural engineering -  Flat slab design
Civil structural engineering - Flat slab design
Satish Narayan
 
Design of column base plates anchor bolt
Design of column base plates anchor boltDesign of column base plates anchor bolt
Design of column base plates anchor bolt
Khaled Eid
 
Structural steel design : beam-columns
Structural steel design : beam-columnsStructural steel design : beam-columns
Structural steel design : beam-columns
Timóteo Rocha
 
Design methods for torsional buckling of steel structures
Design methods for torsional buckling of steel structuresDesign methods for torsional buckling of steel structures
Design methods for torsional buckling of steel structures
Begum Emte Ajom
 
Safe pt design
Safe pt designSafe pt design
Safe pt design
Eldho Peter
 
How To Design Concrete Structures Using Eurocode 2
How To Design Concrete Structures Using Eurocode 2How To Design Concrete Structures Using Eurocode 2
How To Design Concrete Structures Using Eurocode 2
Cтроителен Инженер
 
05-Strength of Double Angle Bolted Tension Members (Steel Structural Design &...
05-Strength of Double Angle Bolted Tension Members (Steel Structural Design &...05-Strength of Double Angle Bolted Tension Members (Steel Structural Design &...
05-Strength of Double Angle Bolted Tension Members (Steel Structural Design &...
Hossam Shafiq II
 

What's hot (20)

ACI 318-19 Ingles.pdf
ACI 318-19 Ingles.pdfACI 318-19 Ingles.pdf
ACI 318-19 Ingles.pdf
 
89505650 concrete-beam-and-slab-design-using-prokon
89505650 concrete-beam-and-slab-design-using-prokon89505650 concrete-beam-and-slab-design-using-prokon
89505650 concrete-beam-and-slab-design-using-prokon
 
ETABS manual - Seismic design of steel buildings according to Eurocode 3 & 8
ETABS manual - Seismic design of steel buildings according to Eurocode 3 & 8 ETABS manual - Seismic design of steel buildings according to Eurocode 3 & 8
ETABS manual - Seismic design of steel buildings according to Eurocode 3 & 8
 
19-Examples for Beam Column (Steel Structural Design & Prof. Shehab Mourad)
19-Examples for Beam Column (Steel Structural Design & Prof. Shehab Mourad)19-Examples for Beam Column (Steel Structural Design & Prof. Shehab Mourad)
19-Examples for Beam Column (Steel Structural Design & Prof. Shehab Mourad)
 
37467305 torsion-design-of-beam
37467305 torsion-design-of-beam37467305 torsion-design-of-beam
37467305 torsion-design-of-beam
 
Design of isolated footing by ACI code
Design of isolated footing by ACI codeDesign of isolated footing by ACI code
Design of isolated footing by ACI code
 
Concrete shear wall design
Concrete shear wall designConcrete shear wall design
Concrete shear wall design
 
23-Design of Column Base Plates (Steel Structural Design & Prof. Shehab Mourad)
23-Design of Column Base Plates (Steel Structural Design & Prof. Shehab Mourad)23-Design of Column Base Plates (Steel Structural Design & Prof. Shehab Mourad)
23-Design of Column Base Plates (Steel Structural Design & Prof. Shehab Mourad)
 
Design of columns biaxial bending as per IS 456-2000
Design of columns  biaxial bending as per IS 456-2000Design of columns  biaxial bending as per IS 456-2000
Design of columns biaxial bending as per IS 456-2000
 
Etabs concrete-design
Etabs concrete-designEtabs concrete-design
Etabs concrete-design
 
CE 72.52 - Lecture 7 - Strut and Tie Models
CE 72.52 - Lecture 7 - Strut and Tie ModelsCE 72.52 - Lecture 7 - Strut and Tie Models
CE 72.52 - Lecture 7 - Strut and Tie Models
 
06-Strength of Double Angle Welded Tension Members (Steel Structural Design &...
06-Strength of Double Angle Welded Tension Members (Steel Structural Design &...06-Strength of Double Angle Welded Tension Members (Steel Structural Design &...
06-Strength of Double Angle Welded Tension Members (Steel Structural Design &...
 
6. safe users-guide
6.  safe users-guide6.  safe users-guide
6. safe users-guide
 
Civil structural engineering - Flat slab design
Civil structural engineering -  Flat slab designCivil structural engineering -  Flat slab design
Civil structural engineering - Flat slab design
 
Design of column base plates anchor bolt
Design of column base plates anchor boltDesign of column base plates anchor bolt
Design of column base plates anchor bolt
 
Structural steel design : beam-columns
Structural steel design : beam-columnsStructural steel design : beam-columns
Structural steel design : beam-columns
 
Design methods for torsional buckling of steel structures
Design methods for torsional buckling of steel structuresDesign methods for torsional buckling of steel structures
Design methods for torsional buckling of steel structures
 
Safe pt design
Safe pt designSafe pt design
Safe pt design
 
How To Design Concrete Structures Using Eurocode 2
How To Design Concrete Structures Using Eurocode 2How To Design Concrete Structures Using Eurocode 2
How To Design Concrete Structures Using Eurocode 2
 
05-Strength of Double Angle Bolted Tension Members (Steel Structural Design &...
05-Strength of Double Angle Bolted Tension Members (Steel Structural Design &...05-Strength of Double Angle Bolted Tension Members (Steel Structural Design &...
05-Strength of Double Angle Bolted Tension Members (Steel Structural Design &...
 

Similar to 13-Effective Length of Columns (Steel Structural Design & Prof. Shehab Mourad)

J012326671
J012326671J012326671
J012326671
IOSR Journals
 
DISTANCE TWO LABELING FOR MULTI-STOREY GRAPHS
DISTANCE TWO LABELING FOR MULTI-STOREY GRAPHSDISTANCE TWO LABELING FOR MULTI-STOREY GRAPHS
DISTANCE TWO LABELING FOR MULTI-STOREY GRAPHS
graphhoc
 
IRJET- Comparative Study of Performance of 60 Storey Steel Buildings with...
IRJET-  	  Comparative Study of Performance of 60 Storey Steel Buildings with...IRJET-  	  Comparative Study of Performance of 60 Storey Steel Buildings with...
IRJET- Comparative Study of Performance of 60 Storey Steel Buildings with...
IRJET Journal
 
Analysis of different types of braces and chord connection in (CFST) k -joint...
Analysis of different types of braces and chord connection in (CFST) k -joint...Analysis of different types of braces and chord connection in (CFST) k -joint...
Analysis of different types of braces and chord connection in (CFST) k -joint...
IRJET Journal
 
Parametric study on behaviour of box girder bridges using CSi Bridge
Parametric study on behaviour of box girder bridges using CSi BridgeParametric study on behaviour of box girder bridges using CSi Bridge
Parametric study on behaviour of box girder bridges using CSi Bridge
IRJET Journal
 
Structur e very helpfull
Structur e very helpfullStructur e very helpfull
Structur e very helpfull
Prionath Roy
 
Civil engineering mock test
Civil engineering mock testCivil engineering mock test
Civil engineering mock test
akshay015
 
Paper id 71201961
Paper id 71201961Paper id 71201961
Paper id 71201961
IJRAT
 
Structural engineering ii
Structural engineering iiStructural engineering ii
Structural engineering ii
Shekh Muhsen Uddin Ahmed
 
Verification of areas of i.s. rolled steel sections
Verification of areas of i.s. rolled steel sectionsVerification of areas of i.s. rolled steel sections
Verification of areas of i.s. rolled steel sections
eSAT Journals
 
Verification of areas of i.s. rolled steel sections
Verification of areas of i.s. rolled steel sectionsVerification of areas of i.s. rolled steel sections
Verification of areas of i.s. rolled steel sections
eSAT Publishing House
 
IRJET - Study on Horizontal Curved Bridge – State of Art Literature Review
IRJET - Study on Horizontal Curved Bridge – State of Art Literature ReviewIRJET - Study on Horizontal Curved Bridge – State of Art Literature Review
IRJET - Study on Horizontal Curved Bridge – State of Art Literature Review
IRJET Journal
 
Cee 311(5)
Cee 311(5)Cee 311(5)
Cee 311(5)
apudgr8
 
EQ21.pdf
EQ21.pdfEQ21.pdf
Sd i-module3- rajesh sir
Sd i-module3- rajesh sirSd i-module3- rajesh sir
Sd i-module3- rajesh sir
SHAMJITH KM
 
IRJET-Study on Behaviour of Retrofitted RC Beam-Column Exterior Joints with G...
IRJET-Study on Behaviour of Retrofitted RC Beam-Column Exterior Joints with G...IRJET-Study on Behaviour of Retrofitted RC Beam-Column Exterior Joints with G...
IRJET-Study on Behaviour of Retrofitted RC Beam-Column Exterior Joints with G...
IRJET Journal
 
EQ06.pdf
EQ06.pdfEQ06.pdf
EQ06.pdf
FAzamKhanAyon1
 
Explanatory Examples on Ductile Detailing of RC Buildings.pdf
Explanatory Examples on Ductile Detailing of RC Buildings.pdfExplanatory Examples on Ductile Detailing of RC Buildings.pdf
Explanatory Examples on Ductile Detailing of RC Buildings.pdf
NagaManikantaTatikon
 
تصميم المنشآت المعنديه - د-سعد الدين مصطفي.pdf
تصميم المنشآت المعنديه - د-سعد الدين مصطفي.pdfتصميم المنشآت المعنديه - د-سعد الدين مصطفي.pdf
تصميم المنشآت المعنديه - د-سعد الدين مصطفي.pdf
HUSAM63
 
Serr calculation
Serr calculationSerr calculation
Serr calculation
vlpham
 

Similar to 13-Effective Length of Columns (Steel Structural Design & Prof. Shehab Mourad) (20)

J012326671
J012326671J012326671
J012326671
 
DISTANCE TWO LABELING FOR MULTI-STOREY GRAPHS
DISTANCE TWO LABELING FOR MULTI-STOREY GRAPHSDISTANCE TWO LABELING FOR MULTI-STOREY GRAPHS
DISTANCE TWO LABELING FOR MULTI-STOREY GRAPHS
 
IRJET- Comparative Study of Performance of 60 Storey Steel Buildings with...
IRJET-  	  Comparative Study of Performance of 60 Storey Steel Buildings with...IRJET-  	  Comparative Study of Performance of 60 Storey Steel Buildings with...
IRJET- Comparative Study of Performance of 60 Storey Steel Buildings with...
 
Analysis of different types of braces and chord connection in (CFST) k -joint...
Analysis of different types of braces and chord connection in (CFST) k -joint...Analysis of different types of braces and chord connection in (CFST) k -joint...
Analysis of different types of braces and chord connection in (CFST) k -joint...
 
Parametric study on behaviour of box girder bridges using CSi Bridge
Parametric study on behaviour of box girder bridges using CSi BridgeParametric study on behaviour of box girder bridges using CSi Bridge
Parametric study on behaviour of box girder bridges using CSi Bridge
 
Structur e very helpfull
Structur e very helpfullStructur e very helpfull
Structur e very helpfull
 
Civil engineering mock test
Civil engineering mock testCivil engineering mock test
Civil engineering mock test
 
Paper id 71201961
Paper id 71201961Paper id 71201961
Paper id 71201961
 
Structural engineering ii
Structural engineering iiStructural engineering ii
Structural engineering ii
 
Verification of areas of i.s. rolled steel sections
Verification of areas of i.s. rolled steel sectionsVerification of areas of i.s. rolled steel sections
Verification of areas of i.s. rolled steel sections
 
Verification of areas of i.s. rolled steel sections
Verification of areas of i.s. rolled steel sectionsVerification of areas of i.s. rolled steel sections
Verification of areas of i.s. rolled steel sections
 
IRJET - Study on Horizontal Curved Bridge – State of Art Literature Review
IRJET - Study on Horizontal Curved Bridge – State of Art Literature ReviewIRJET - Study on Horizontal Curved Bridge – State of Art Literature Review
IRJET - Study on Horizontal Curved Bridge – State of Art Literature Review
 
Cee 311(5)
Cee 311(5)Cee 311(5)
Cee 311(5)
 
EQ21.pdf
EQ21.pdfEQ21.pdf
EQ21.pdf
 
Sd i-module3- rajesh sir
Sd i-module3- rajesh sirSd i-module3- rajesh sir
Sd i-module3- rajesh sir
 
IRJET-Study on Behaviour of Retrofitted RC Beam-Column Exterior Joints with G...
IRJET-Study on Behaviour of Retrofitted RC Beam-Column Exterior Joints with G...IRJET-Study on Behaviour of Retrofitted RC Beam-Column Exterior Joints with G...
IRJET-Study on Behaviour of Retrofitted RC Beam-Column Exterior Joints with G...
 
EQ06.pdf
EQ06.pdfEQ06.pdf
EQ06.pdf
 
Explanatory Examples on Ductile Detailing of RC Buildings.pdf
Explanatory Examples on Ductile Detailing of RC Buildings.pdfExplanatory Examples on Ductile Detailing of RC Buildings.pdf
Explanatory Examples on Ductile Detailing of RC Buildings.pdf
 
تصميم المنشآت المعنديه - د-سعد الدين مصطفي.pdf
تصميم المنشآت المعنديه - د-سعد الدين مصطفي.pdfتصميم المنشآت المعنديه - د-سعد الدين مصطفي.pdf
تصميم المنشآت المعنديه - د-سعد الدين مصطفي.pdf
 
Serr calculation
Serr calculationSerr calculation
Serr calculation
 

More from Hossam Shafiq II

Basics of Foundation Engineering هندسة الأساسات & Eng. Ahmed S. Al-Agha
Basics of Foundation Engineering هندسة الأساسات & Eng. Ahmed S. Al-AghaBasics of Foundation Engineering هندسة الأساسات & Eng. Ahmed S. Al-Agha
Basics of Foundation Engineering هندسة الأساسات & Eng. Ahmed S. Al-Agha
Hossam Shafiq II
 
Ch8 Truss Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metwally ...
Ch8 Truss Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metwally ...Ch8 Truss Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metwally ...
Ch8 Truss Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metwally ...
Hossam Shafiq II
 
Ch7 Box Girder Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metw...
Ch7 Box Girder Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metw...Ch7 Box Girder Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metw...
Ch7 Box Girder Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metw...
Hossam Shafiq II
 
Ch6 Composite Plate Girder Bridges (Steel Bridges تصميم الكباري المعدنية & Pr...
Ch6 Composite Plate Girder Bridges (Steel Bridges تصميم الكباري المعدنية & Pr...Ch6 Composite Plate Girder Bridges (Steel Bridges تصميم الكباري المعدنية & Pr...
Ch6 Composite Plate Girder Bridges (Steel Bridges تصميم الكباري المعدنية & Pr...
Hossam Shafiq II
 
Ch5 Plate Girder Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Me...
Ch5 Plate Girder Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Me...Ch5 Plate Girder Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Me...
Ch5 Plate Girder Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Me...
Hossam Shafiq II
 
Ch4 Bridge Floors (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metwally ...
Ch4 Bridge Floors (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metwally ...Ch4 Bridge Floors (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metwally ...
Ch4 Bridge Floors (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metwally ...
Hossam Shafiq II
 
Ch3 Design Considerations (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. M...
Ch3 Design Considerations (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. M...Ch3 Design Considerations (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. M...
Ch3 Design Considerations (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. M...
Hossam Shafiq II
 
Ch2 Design Loads on Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr....
Ch2 Design Loads on Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr....Ch2 Design Loads on Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr....
Ch2 Design Loads on Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr....
Hossam Shafiq II
 
Ch1 Introduction (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metwally A...
Ch1 Introduction (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metwally A...Ch1 Introduction (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metwally A...
Ch1 Introduction (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metwally A...
Hossam Shafiq II
 
Lec05 STRUCTURE SYSTEMS to resist EARTHQUAKE (Earthquake Engineering هندسة ال...
Lec05 STRUCTURE SYSTEMS to resist EARTHQUAKE (Earthquake Engineering هندسة ال...Lec05 STRUCTURE SYSTEMS to resist EARTHQUAKE (Earthquake Engineering هندسة ال...
Lec05 STRUCTURE SYSTEMS to resist EARTHQUAKE (Earthquake Engineering هندسة ال...
Hossam Shafiq II
 
Lec04 Earthquake Force Using Response Specturum Method (2) (Earthquake Engine...
Lec04 Earthquake Force Using Response Specturum Method (2) (Earthquake Engine...Lec04 Earthquake Force Using Response Specturum Method (2) (Earthquake Engine...
Lec04 Earthquake Force Using Response Specturum Method (2) (Earthquake Engine...
Hossam Shafiq II
 
Lec03 Earthquake Force Using Response Specturum Method (1) (Earthquake Engine...
Lec03 Earthquake Force Using Response Specturum Method (1) (Earthquake Engine...Lec03 Earthquake Force Using Response Specturum Method (1) (Earthquake Engine...
Lec03 Earthquake Force Using Response Specturum Method (1) (Earthquake Engine...
Hossam Shafiq II
 
Lec02 Earthquake Damage to Concrete Structure (Earthquake Engineering هندسة ا...
Lec02 Earthquake Damage to Concrete Structure (Earthquake Engineering هندسة ا...Lec02 Earthquake Damage to Concrete Structure (Earthquake Engineering هندسة ا...
Lec02 Earthquake Damage to Concrete Structure (Earthquake Engineering هندسة ا...
Hossam Shafiq II
 
Lec01 Design of RC Structures under lateral load (Earthquake Engineering هندس...
Lec01 Design of RC Structures under lateral load (Earthquake Engineering هندس...Lec01 Design of RC Structures under lateral load (Earthquake Engineering هندس...
Lec01 Design of RC Structures under lateral load (Earthquake Engineering هندس...
Hossam Shafiq II
 
Lec13 Continuous Beams and One Way Slabs(3) Footings (Reinforced Concrete Des...
Lec13 Continuous Beams and One Way Slabs(3) Footings (Reinforced Concrete Des...Lec13 Continuous Beams and One Way Slabs(3) Footings (Reinforced Concrete Des...
Lec13 Continuous Beams and One Way Slabs(3) Footings (Reinforced Concrete Des...
Hossam Shafiq II
 
Lec12 Continuous Beams and One Way Slabs(2) Columns (Reinforced Concrete Desi...
Lec12 Continuous Beams and One Way Slabs(2) Columns (Reinforced Concrete Desi...Lec12 Continuous Beams and One Way Slabs(2) Columns (Reinforced Concrete Desi...
Lec12 Continuous Beams and One Way Slabs(2) Columns (Reinforced Concrete Desi...
Hossam Shafiq II
 
Lec11 Continuous Beams and One Way Slabs(1) (Reinforced Concrete Design I & P...
Lec11 Continuous Beams and One Way Slabs(1) (Reinforced Concrete Design I & P...Lec11 Continuous Beams and One Way Slabs(1) (Reinforced Concrete Design I & P...
Lec11 Continuous Beams and One Way Slabs(1) (Reinforced Concrete Design I & P...
Hossam Shafiq II
 
Lec10 Bond and Development Length (Reinforced Concrete Design I & Prof. Abdel...
Lec10 Bond and Development Length (Reinforced Concrete Design I & Prof. Abdel...Lec10 Bond and Development Length (Reinforced Concrete Design I & Prof. Abdel...
Lec10 Bond and Development Length (Reinforced Concrete Design I & Prof. Abdel...
Hossam Shafiq II
 
Lec09 Shear in RC Beams (Reinforced Concrete Design I & Prof. Abdelhamid Charif)
Lec09 Shear in RC Beams (Reinforced Concrete Design I & Prof. Abdelhamid Charif)Lec09 Shear in RC Beams (Reinforced Concrete Design I & Prof. Abdelhamid Charif)
Lec09 Shear in RC Beams (Reinforced Concrete Design I & Prof. Abdelhamid Charif)
Hossam Shafiq II
 
Lec07 Analysis and Design of Doubly Reinforced Beam (Reinforced Concrete Desi...
Lec07 Analysis and Design of Doubly Reinforced Beam (Reinforced Concrete Desi...Lec07 Analysis and Design of Doubly Reinforced Beam (Reinforced Concrete Desi...
Lec07 Analysis and Design of Doubly Reinforced Beam (Reinforced Concrete Desi...
Hossam Shafiq II
 

More from Hossam Shafiq II (20)

Basics of Foundation Engineering هندسة الأساسات & Eng. Ahmed S. Al-Agha
Basics of Foundation Engineering هندسة الأساسات & Eng. Ahmed S. Al-AghaBasics of Foundation Engineering هندسة الأساسات & Eng. Ahmed S. Al-Agha
Basics of Foundation Engineering هندسة الأساسات & Eng. Ahmed S. Al-Agha
 
Ch8 Truss Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metwally ...
Ch8 Truss Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metwally ...Ch8 Truss Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metwally ...
Ch8 Truss Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metwally ...
 
Ch7 Box Girder Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metw...
Ch7 Box Girder Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metw...Ch7 Box Girder Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metw...
Ch7 Box Girder Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metw...
 
Ch6 Composite Plate Girder Bridges (Steel Bridges تصميم الكباري المعدنية & Pr...
Ch6 Composite Plate Girder Bridges (Steel Bridges تصميم الكباري المعدنية & Pr...Ch6 Composite Plate Girder Bridges (Steel Bridges تصميم الكباري المعدنية & Pr...
Ch6 Composite Plate Girder Bridges (Steel Bridges تصميم الكباري المعدنية & Pr...
 
Ch5 Plate Girder Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Me...
Ch5 Plate Girder Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Me...Ch5 Plate Girder Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Me...
Ch5 Plate Girder Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Me...
 
Ch4 Bridge Floors (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metwally ...
Ch4 Bridge Floors (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metwally ...Ch4 Bridge Floors (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metwally ...
Ch4 Bridge Floors (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metwally ...
 
Ch3 Design Considerations (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. M...
Ch3 Design Considerations (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. M...Ch3 Design Considerations (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. M...
Ch3 Design Considerations (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. M...
 
Ch2 Design Loads on Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr....
Ch2 Design Loads on Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr....Ch2 Design Loads on Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr....
Ch2 Design Loads on Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr....
 
Ch1 Introduction (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metwally A...
Ch1 Introduction (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metwally A...Ch1 Introduction (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metwally A...
Ch1 Introduction (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metwally A...
 
Lec05 STRUCTURE SYSTEMS to resist EARTHQUAKE (Earthquake Engineering هندسة ال...
Lec05 STRUCTURE SYSTEMS to resist EARTHQUAKE (Earthquake Engineering هندسة ال...Lec05 STRUCTURE SYSTEMS to resist EARTHQUAKE (Earthquake Engineering هندسة ال...
Lec05 STRUCTURE SYSTEMS to resist EARTHQUAKE (Earthquake Engineering هندسة ال...
 
Lec04 Earthquake Force Using Response Specturum Method (2) (Earthquake Engine...
Lec04 Earthquake Force Using Response Specturum Method (2) (Earthquake Engine...Lec04 Earthquake Force Using Response Specturum Method (2) (Earthquake Engine...
Lec04 Earthquake Force Using Response Specturum Method (2) (Earthquake Engine...
 
Lec03 Earthquake Force Using Response Specturum Method (1) (Earthquake Engine...
Lec03 Earthquake Force Using Response Specturum Method (1) (Earthquake Engine...Lec03 Earthquake Force Using Response Specturum Method (1) (Earthquake Engine...
Lec03 Earthquake Force Using Response Specturum Method (1) (Earthquake Engine...
 
Lec02 Earthquake Damage to Concrete Structure (Earthquake Engineering هندسة ا...
Lec02 Earthquake Damage to Concrete Structure (Earthquake Engineering هندسة ا...Lec02 Earthquake Damage to Concrete Structure (Earthquake Engineering هندسة ا...
Lec02 Earthquake Damage to Concrete Structure (Earthquake Engineering هندسة ا...
 
Lec01 Design of RC Structures under lateral load (Earthquake Engineering هندس...
Lec01 Design of RC Structures under lateral load (Earthquake Engineering هندس...Lec01 Design of RC Structures under lateral load (Earthquake Engineering هندس...
Lec01 Design of RC Structures under lateral load (Earthquake Engineering هندس...
 
Lec13 Continuous Beams and One Way Slabs(3) Footings (Reinforced Concrete Des...
Lec13 Continuous Beams and One Way Slabs(3) Footings (Reinforced Concrete Des...Lec13 Continuous Beams and One Way Slabs(3) Footings (Reinforced Concrete Des...
Lec13 Continuous Beams and One Way Slabs(3) Footings (Reinforced Concrete Des...
 
Lec12 Continuous Beams and One Way Slabs(2) Columns (Reinforced Concrete Desi...
Lec12 Continuous Beams and One Way Slabs(2) Columns (Reinforced Concrete Desi...Lec12 Continuous Beams and One Way Slabs(2) Columns (Reinforced Concrete Desi...
Lec12 Continuous Beams and One Way Slabs(2) Columns (Reinforced Concrete Desi...
 
Lec11 Continuous Beams and One Way Slabs(1) (Reinforced Concrete Design I & P...
Lec11 Continuous Beams and One Way Slabs(1) (Reinforced Concrete Design I & P...Lec11 Continuous Beams and One Way Slabs(1) (Reinforced Concrete Design I & P...
Lec11 Continuous Beams and One Way Slabs(1) (Reinforced Concrete Design I & P...
 
Lec10 Bond and Development Length (Reinforced Concrete Design I & Prof. Abdel...
Lec10 Bond and Development Length (Reinforced Concrete Design I & Prof. Abdel...Lec10 Bond and Development Length (Reinforced Concrete Design I & Prof. Abdel...
Lec10 Bond and Development Length (Reinforced Concrete Design I & Prof. Abdel...
 
Lec09 Shear in RC Beams (Reinforced Concrete Design I & Prof. Abdelhamid Charif)
Lec09 Shear in RC Beams (Reinforced Concrete Design I & Prof. Abdelhamid Charif)Lec09 Shear in RC Beams (Reinforced Concrete Design I & Prof. Abdelhamid Charif)
Lec09 Shear in RC Beams (Reinforced Concrete Design I & Prof. Abdelhamid Charif)
 
Lec07 Analysis and Design of Doubly Reinforced Beam (Reinforced Concrete Desi...
Lec07 Analysis and Design of Doubly Reinforced Beam (Reinforced Concrete Desi...Lec07 Analysis and Design of Doubly Reinforced Beam (Reinforced Concrete Desi...
Lec07 Analysis and Design of Doubly Reinforced Beam (Reinforced Concrete Desi...
 

Recently uploaded

Design and optimization of ion propulsion drone
Design and optimization of ion propulsion droneDesign and optimization of ion propulsion drone
Design and optimization of ion propulsion drone
bjmsejournal
 
一比一原版(osu毕业证书)美国俄勒冈州立大学毕业证如何办理
一比一原版(osu毕业证书)美国俄勒冈州立大学毕业证如何办理一比一原版(osu毕业证书)美国俄勒冈州立大学毕业证如何办理
一比一原版(osu毕业证书)美国俄勒冈州立大学毕业证如何办理
upoux
 
132/33KV substation case study Presentation
132/33KV substation case study Presentation132/33KV substation case study Presentation
132/33KV substation case study Presentation
kandramariana6
 
2008 BUILDING CONSTRUCTION Illustrated - Ching Chapter 02 The Building.pdf
2008 BUILDING CONSTRUCTION Illustrated - Ching Chapter 02 The Building.pdf2008 BUILDING CONSTRUCTION Illustrated - Ching Chapter 02 The Building.pdf
2008 BUILDING CONSTRUCTION Illustrated - Ching Chapter 02 The Building.pdf
Yasser Mahgoub
 
Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...
Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...
Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...
IJECEIAES
 
1FIDIC-CONSTRUCTION-CONTRACT-2ND-ED-2017-RED-BOOK.pdf
1FIDIC-CONSTRUCTION-CONTRACT-2ND-ED-2017-RED-BOOK.pdf1FIDIC-CONSTRUCTION-CONTRACT-2ND-ED-2017-RED-BOOK.pdf
1FIDIC-CONSTRUCTION-CONTRACT-2ND-ED-2017-RED-BOOK.pdf
MadhavJungKarki
 
Software Engineering and Project Management - Introduction, Modeling Concepts...
Software Engineering and Project Management - Introduction, Modeling Concepts...Software Engineering and Project Management - Introduction, Modeling Concepts...
Software Engineering and Project Management - Introduction, Modeling Concepts...
Prakhyath Rai
 
22CYT12-Unit-V-E Waste and its Management.ppt
22CYT12-Unit-V-E Waste and its Management.ppt22CYT12-Unit-V-E Waste and its Management.ppt
22CYT12-Unit-V-E Waste and its Management.ppt
KrishnaveniKrishnara1
 
4. Mosca vol I -Fisica-Tipler-5ta-Edicion-Vol-1.pdf
4. Mosca vol I -Fisica-Tipler-5ta-Edicion-Vol-1.pdf4. Mosca vol I -Fisica-Tipler-5ta-Edicion-Vol-1.pdf
4. Mosca vol I -Fisica-Tipler-5ta-Edicion-Vol-1.pdf
Gino153088
 
Software Engineering and Project Management - Software Testing + Agile Method...
Software Engineering and Project Management - Software Testing + Agile Method...Software Engineering and Project Management - Software Testing + Agile Method...
Software Engineering and Project Management - Software Testing + Agile Method...
Prakhyath Rai
 
一比一原版(爱大毕业证书)爱荷华大学毕业证如何办理
一比一原版(爱大毕业证书)爱荷华大学毕业证如何办理一比一原版(爱大毕业证书)爱荷华大学毕业证如何办理
一比一原版(爱大毕业证书)爱荷华大学毕业证如何办理
nedcocy
 
ITSM Integration with MuleSoft.pptx
ITSM  Integration with MuleSoft.pptxITSM  Integration with MuleSoft.pptx
ITSM Integration with MuleSoft.pptx
VANDANAMOHANGOUDA
 
原版制作(Humboldt毕业证书)柏林大学毕业证学位证一模一样
原版制作(Humboldt毕业证书)柏林大学毕业证学位证一模一样原版制作(Humboldt毕业证书)柏林大学毕业证学位证一模一样
原版制作(Humboldt毕业证书)柏林大学毕业证学位证一模一样
ydzowc
 
Electric vehicle and photovoltaic advanced roles in enhancing the financial p...
Electric vehicle and photovoltaic advanced roles in enhancing the financial p...Electric vehicle and photovoltaic advanced roles in enhancing the financial p...
Electric vehicle and photovoltaic advanced roles in enhancing the financial p...
IJECEIAES
 
Optimizing Gradle Builds - Gradle DPE Tour Berlin 2024
Optimizing Gradle Builds - Gradle DPE Tour Berlin 2024Optimizing Gradle Builds - Gradle DPE Tour Berlin 2024
Optimizing Gradle Builds - Gradle DPE Tour Berlin 2024
Sinan KOZAK
 
Generative AI Use cases applications solutions and implementation.pdf
Generative AI Use cases applications solutions and implementation.pdfGenerative AI Use cases applications solutions and implementation.pdf
Generative AI Use cases applications solutions and implementation.pdf
mahaffeycheryld
 
Comparative analysis between traditional aquaponics and reconstructed aquapon...
Comparative analysis between traditional aquaponics and reconstructed aquapon...Comparative analysis between traditional aquaponics and reconstructed aquapon...
Comparative analysis between traditional aquaponics and reconstructed aquapon...
bijceesjournal
 
Prediction of Electrical Energy Efficiency Using Information on Consumer's Ac...
Prediction of Electrical Energy Efficiency Using Information on Consumer's Ac...Prediction of Electrical Energy Efficiency Using Information on Consumer's Ac...
Prediction of Electrical Energy Efficiency Using Information on Consumer's Ac...
PriyankaKilaniya
 
Embedded machine learning-based road conditions and driving behavior monitoring
Embedded machine learning-based road conditions and driving behavior monitoringEmbedded machine learning-based road conditions and driving behavior monitoring
Embedded machine learning-based road conditions and driving behavior monitoring
IJECEIAES
 
AI for Legal Research with applications, tools
AI for Legal Research with applications, toolsAI for Legal Research with applications, tools
AI for Legal Research with applications, tools
mahaffeycheryld
 

Recently uploaded (20)

Design and optimization of ion propulsion drone
Design and optimization of ion propulsion droneDesign and optimization of ion propulsion drone
Design and optimization of ion propulsion drone
 
一比一原版(osu毕业证书)美国俄勒冈州立大学毕业证如何办理
一比一原版(osu毕业证书)美国俄勒冈州立大学毕业证如何办理一比一原版(osu毕业证书)美国俄勒冈州立大学毕业证如何办理
一比一原版(osu毕业证书)美国俄勒冈州立大学毕业证如何办理
 
132/33KV substation case study Presentation
132/33KV substation case study Presentation132/33KV substation case study Presentation
132/33KV substation case study Presentation
 
2008 BUILDING CONSTRUCTION Illustrated - Ching Chapter 02 The Building.pdf
2008 BUILDING CONSTRUCTION Illustrated - Ching Chapter 02 The Building.pdf2008 BUILDING CONSTRUCTION Illustrated - Ching Chapter 02 The Building.pdf
2008 BUILDING CONSTRUCTION Illustrated - Ching Chapter 02 The Building.pdf
 
Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...
Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...
Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...
 
1FIDIC-CONSTRUCTION-CONTRACT-2ND-ED-2017-RED-BOOK.pdf
1FIDIC-CONSTRUCTION-CONTRACT-2ND-ED-2017-RED-BOOK.pdf1FIDIC-CONSTRUCTION-CONTRACT-2ND-ED-2017-RED-BOOK.pdf
1FIDIC-CONSTRUCTION-CONTRACT-2ND-ED-2017-RED-BOOK.pdf
 
Software Engineering and Project Management - Introduction, Modeling Concepts...
Software Engineering and Project Management - Introduction, Modeling Concepts...Software Engineering and Project Management - Introduction, Modeling Concepts...
Software Engineering and Project Management - Introduction, Modeling Concepts...
 
22CYT12-Unit-V-E Waste and its Management.ppt
22CYT12-Unit-V-E Waste and its Management.ppt22CYT12-Unit-V-E Waste and its Management.ppt
22CYT12-Unit-V-E Waste and its Management.ppt
 
4. Mosca vol I -Fisica-Tipler-5ta-Edicion-Vol-1.pdf
4. Mosca vol I -Fisica-Tipler-5ta-Edicion-Vol-1.pdf4. Mosca vol I -Fisica-Tipler-5ta-Edicion-Vol-1.pdf
4. Mosca vol I -Fisica-Tipler-5ta-Edicion-Vol-1.pdf
 
Software Engineering and Project Management - Software Testing + Agile Method...
Software Engineering and Project Management - Software Testing + Agile Method...Software Engineering and Project Management - Software Testing + Agile Method...
Software Engineering and Project Management - Software Testing + Agile Method...
 
一比一原版(爱大毕业证书)爱荷华大学毕业证如何办理
一比一原版(爱大毕业证书)爱荷华大学毕业证如何办理一比一原版(爱大毕业证书)爱荷华大学毕业证如何办理
一比一原版(爱大毕业证书)爱荷华大学毕业证如何办理
 
ITSM Integration with MuleSoft.pptx
ITSM  Integration with MuleSoft.pptxITSM  Integration with MuleSoft.pptx
ITSM Integration with MuleSoft.pptx
 
原版制作(Humboldt毕业证书)柏林大学毕业证学位证一模一样
原版制作(Humboldt毕业证书)柏林大学毕业证学位证一模一样原版制作(Humboldt毕业证书)柏林大学毕业证学位证一模一样
原版制作(Humboldt毕业证书)柏林大学毕业证学位证一模一样
 
Electric vehicle and photovoltaic advanced roles in enhancing the financial p...
Electric vehicle and photovoltaic advanced roles in enhancing the financial p...Electric vehicle and photovoltaic advanced roles in enhancing the financial p...
Electric vehicle and photovoltaic advanced roles in enhancing the financial p...
 
Optimizing Gradle Builds - Gradle DPE Tour Berlin 2024
Optimizing Gradle Builds - Gradle DPE Tour Berlin 2024Optimizing Gradle Builds - Gradle DPE Tour Berlin 2024
Optimizing Gradle Builds - Gradle DPE Tour Berlin 2024
 
Generative AI Use cases applications solutions and implementation.pdf
Generative AI Use cases applications solutions and implementation.pdfGenerative AI Use cases applications solutions and implementation.pdf
Generative AI Use cases applications solutions and implementation.pdf
 
Comparative analysis between traditional aquaponics and reconstructed aquapon...
Comparative analysis between traditional aquaponics and reconstructed aquapon...Comparative analysis between traditional aquaponics and reconstructed aquapon...
Comparative analysis between traditional aquaponics and reconstructed aquapon...
 
Prediction of Electrical Energy Efficiency Using Information on Consumer's Ac...
Prediction of Electrical Energy Efficiency Using Information on Consumer's Ac...Prediction of Electrical Energy Efficiency Using Information on Consumer's Ac...
Prediction of Electrical Energy Efficiency Using Information on Consumer's Ac...
 
Embedded machine learning-based road conditions and driving behavior monitoring
Embedded machine learning-based road conditions and driving behavior monitoringEmbedded machine learning-based road conditions and driving behavior monitoring
Embedded machine learning-based road conditions and driving behavior monitoring
 
AI for Legal Research with applications, tools
AI for Legal Research with applications, toolsAI for Legal Research with applications, tools
AI for Legal Research with applications, tools
 

13-Effective Length of Columns (Steel Structural Design & Prof. Shehab Mourad)

  • 1. 1 Prepared by Prof. Shehab Mourad – Department of Civil Eng. - KSU Effective Length of Columns The effective column length (the equivalent half wave of buckling length), depends on; 1) The fixed end conditions (fixed, hinged or free ends), of the column (K factor). 2) The framing condition, whether it is braced or unbraced L L Braced Frame (Sway prevented) Unbraced Frame (Sway Permitted) P P P P 0.5 < K< 1.0 1.0 < K 5.0 K≤ 1 K≥ 2 Ib
  • 2. 2 Prepared by Prof. Shehab Mourad – Department of Civil Eng. - KSU 3) The column - beam connections, and the relative stiffnesses of columns to beams at each end of the column S (I/L) columns G = S (I/L) beams Note : G = 10 for hinged (pinned) support G = 1.0 for fixed support For braced Frame Km = 3 Gi Gj + 1.4 (Gi + Gj) + 0.64 3 Gi Gj + 2 (Gi+Gj) + 1.28 For unbraced Frame Km = 1.6 Gi Gj + 4 (Gi+Gj) + 7.5 Gi + G j + 7.5 Or by using charts:
  • 3. 3 Prepared by Prof. Shehab Mourad – Department of Civil Eng. - KSU Example For the shown two storey frame with the indicated relative Inertias, computed the Buckling length factor (K) for columns 1, 2 and 3. Solution: G1= 10 for hinged support G3 = G6 = 1.0 for fixed support G2 = (I/5) = 0.60 (2I /6) G4 = ( 2I/5 + I/3 ) = 1.257 (2I/6 + 2I/8) G5 = (I/3) = 1.332 (2I/8) For Column 1, (unbraced frame) Values from charts K1 = 1.6 x 10 x 0.6 + 4 (10 +0.6) + 7.5 = 1.81 1.80 10 + 0.60 + 7.5 For Column 2, (unbraced frame) K2 = 1.6 x 1 x 1.257 + 4 (1 + 1.257) + 7.5 = 1.378 1.375 1 + 1.257 + 7.5 For Column 3, (braced Frame) K3 = ( 3 x 1.257x1.332) + 1.4 (1.257 + 1.332) + 0.64 = 0.81 0.80 3 x 1.257 x 1.332 + 2 ( 1.257 + 1.332) + 1.28 5 m 3m 6m 8m 1 2 3 4 5 6 7 8 I 2I 2I 2I 2I I I I1 2 3