chapter 6: analysis and design of beam-columns · 5 interaction formula pu = pnt + b2 plt • pnt:...
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![Page 1: Chapter 6: Analysis and Design of Beam-Columns · 5 Interaction Formula Pu = Pnt + B2 Plt • Pnt: Axial load assuming that no sidesway occurs (no translation). • Plt :Axial load](https://reader031.vdocument.in/reader031/viewer/2022013006/5af30ef87f8b9a8b4c90f829/html5/thumbnails/1.jpg)
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Chapter 6: Analysis and Design of Beam-Columns
Dr. Hasan Katkhuda
Steel Design
STEEL DESIGN
Introduction
• Beam-columns are members that are subjected to bending and axial forces. (Tension or Compression)
Dr. Hasan Katkhuda
Steel Design
![Page 2: Chapter 6: Analysis and Design of Beam-Columns · 5 Interaction Formula Pu = Pnt + B2 Plt • Pnt: Axial load assuming that no sidesway occurs (no translation). • Plt :Axial load](https://reader031.vdocument.in/reader031/viewer/2022013006/5af30ef87f8b9a8b4c90f829/html5/thumbnails/2.jpg)
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Introduction
• First Order (F.O) Analysis: Structural analysis using undeformed shape of the structure.
• Second Order (S.O) Analysis: Structural analysis considering geometric changes due to deformations in structural formulations.
Dr. Hasan Katkhuda
Steel Design
Introduction
Dr. Hasan Katkhuda
Steel Design
![Page 3: Chapter 6: Analysis and Design of Beam-Columns · 5 Interaction Formula Pu = Pnt + B2 Plt • Pnt: Axial load assuming that no sidesway occurs (no translation). • Plt :Axial load](https://reader031.vdocument.in/reader031/viewer/2022013006/5af30ef87f8b9a8b4c90f829/html5/thumbnails/3.jpg)
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Introduction
Dr. Hasan Katkhuda
Steel Design
Introduction
• Second Order:
1. Use computers and make a second order analysis to determine the maximum factored load strength.
2. Use First Order analysis and amplify the moments obtained with some amplification factors.
Dr. Hasan Katkhuda
Steel Design
![Page 4: Chapter 6: Analysis and Design of Beam-Columns · 5 Interaction Formula Pu = Pnt + B2 Plt • Pnt: Axial load assuming that no sidesway occurs (no translation). • Plt :Axial load](https://reader031.vdocument.in/reader031/viewer/2022013006/5af30ef87f8b9a8b4c90f829/html5/thumbnails/4.jpg)
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Interaction Formula
• Chapter H in the specifications in the manual.
1. .
2. .
Dr. Hasan Katkhuda
Steel Design
Interaction Formula
Mu = B1 Mnt + B2 Mlt
• Mnt: Maximum moment assuming that no sidesway occurs (no translation) (First order).
• Mlt :Maximum moment caused by sidesway (lateral translation) (First order)
• B1 : Amplification factor for the moments occurring in member when it is braced against sidesway.
• B2 : Amplification factor for moments resulting from sidesway.
Dr. Hasan Katkhuda
Steel Design
![Page 5: Chapter 6: Analysis and Design of Beam-Columns · 5 Interaction Formula Pu = Pnt + B2 Plt • Pnt: Axial load assuming that no sidesway occurs (no translation). • Plt :Axial load](https://reader031.vdocument.in/reader031/viewer/2022013006/5af30ef87f8b9a8b4c90f829/html5/thumbnails/5.jpg)
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Interaction Formula
Pu = Pnt + B2 Plt
• Pnt: Axial load assuming that no sidesway occurs (no translation).
• Plt :Axial load caused by sidesway (lateral translation.
• B2 : Amplification factor for moments resulting from sidesway.
Dr. Hasan Katkhuda
Steel Design
Interaction Formula
• K < 1.0 (BRACED FRAME)
• Cm : Modification factor due to maximum moment depends on the distribution of bending moment within the member.
Dr. Hasan Katkhuda
Steel Design
![Page 6: Chapter 6: Analysis and Design of Beam-Columns · 5 Interaction Formula Pu = Pnt + B2 Plt • Pnt: Axial load assuming that no sidesway occurs (no translation). • Plt :Axial load](https://reader031.vdocument.in/reader031/viewer/2022013006/5af30ef87f8b9a8b4c90f829/html5/thumbnails/6.jpg)
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Interaction Formula
Dr. Hasan Katkhuda
Steel Design
Interaction Formula
Dr. Hasan Katkhuda
Steel Design
![Page 7: Chapter 6: Analysis and Design of Beam-Columns · 5 Interaction Formula Pu = Pnt + B2 Plt • Pnt: Axial load assuming that no sidesway occurs (no translation). • Plt :Axial load](https://reader031.vdocument.in/reader031/viewer/2022013006/5af30ef87f8b9a8b4c90f829/html5/thumbnails/7.jpg)
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Interaction Formula
• Cm:
Dr. Hasan Katkhuda
Steel Design
Interaction Formula
• Cm:
Dr. Hasan Katkhuda
Steel Design
![Page 8: Chapter 6: Analysis and Design of Beam-Columns · 5 Interaction Formula Pu = Pnt + B2 Plt • Pnt: Axial load assuming that no sidesway occurs (no translation). • Plt :Axial load](https://reader031.vdocument.in/reader031/viewer/2022013006/5af30ef87f8b9a8b4c90f829/html5/thumbnails/8.jpg)
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Interaction Formula
• Cm:
1. If there is no transverse loads acting on the member:
• M1 / M2: Ratio of bending moments at the ends of the member.
• M1: Absolute smaller value.
• M2: Absolute larger value.
• Ratio (+ve) when reverse or double curvature.
(-ve) when single curvature.
Dr. Hasan Katkhuda
Steel Design
Interaction Formula
• Cm:
Dr. Hasan Katkhuda
Steel Design
![Page 9: Chapter 6: Analysis and Design of Beam-Columns · 5 Interaction Formula Pu = Pnt + B2 Plt • Pnt: Axial load assuming that no sidesway occurs (no translation). • Plt :Axial load](https://reader031.vdocument.in/reader031/viewer/2022013006/5af30ef87f8b9a8b4c90f829/html5/thumbnails/9.jpg)
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Interaction Formula
• Cm:
2. For transversely loaded members:
Dr. Hasan Katkhuda
Steel Design
Dr. Hasan Katkhuda
Steel Design
![Page 10: Chapter 6: Analysis and Design of Beam-Columns · 5 Interaction Formula Pu = Pnt + B2 Plt • Pnt: Axial load assuming that no sidesway occurs (no translation). • Plt :Axial load](https://reader031.vdocument.in/reader031/viewer/2022013006/5af30ef87f8b9a8b4c90f829/html5/thumbnails/10.jpg)
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Examples (Analysis for Braced Frame)
• Example 1:
• Braced frame.
• Service loads and moments about strong axis are shown.
• A5732, Grade 50
• KxLx = KyLy = 14 ft
Dr. Hasan Katkhuda
Steel Design
Examples (Analysis for Braced Frame)
Dr. Hasan Katkhuda
Steel Design
![Page 11: Chapter 6: Analysis and Design of Beam-Columns · 5 Interaction Formula Pu = Pnt + B2 Plt • Pnt: Axial load assuming that no sidesway occurs (no translation). • Plt :Axial load](https://reader031.vdocument.in/reader031/viewer/2022013006/5af30ef87f8b9a8b4c90f829/html5/thumbnails/11.jpg)
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Examples (Analysis for Braced Frame)
Dr. Hasan Katkhuda
Steel Design
Examples (Analysis for Braced Frame)
Dr. Hasan Katkhuda
Steel Design
![Page 12: Chapter 6: Analysis and Design of Beam-Columns · 5 Interaction Formula Pu = Pnt + B2 Plt • Pnt: Axial load assuming that no sidesway occurs (no translation). • Plt :Axial load](https://reader031.vdocument.in/reader031/viewer/2022013006/5af30ef87f8b9a8b4c90f829/html5/thumbnails/12.jpg)
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Examples (Analysis for Braced Frame)
• Example 2:
• Service live loads are shown.
• Laterally braced at ends.
• Bending about x axis.
• Fy = 50 ksi
Dr. Hasan Katkhuda
Steel Design
Examples (Analysis for Braced Frame)
Dr. Hasan Katkhuda
Steel Design
![Page 13: Chapter 6: Analysis and Design of Beam-Columns · 5 Interaction Formula Pu = Pnt + B2 Plt • Pnt: Axial load assuming that no sidesway occurs (no translation). • Plt :Axial load](https://reader031.vdocument.in/reader031/viewer/2022013006/5af30ef87f8b9a8b4c90f829/html5/thumbnails/13.jpg)
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Examples (Analysis for Braced Frame)
Dr. Hasan Katkhuda
Steel Design
Examples (Analysis for Braced Frame)
• Cb = 1.32
• >
Dr. Hasan Katkhuda
Steel Design
![Page 14: Chapter 6: Analysis and Design of Beam-Columns · 5 Interaction Formula Pu = Pnt + B2 Plt • Pnt: Axial load assuming that no sidesway occurs (no translation). • Plt :Axial load](https://reader031.vdocument.in/reader031/viewer/2022013006/5af30ef87f8b9a8b4c90f829/html5/thumbnails/14.jpg)
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Examples (Analysis for Braced Frame)
• Example 3:
• Service Loads and Moments are shown.
• Use Kx = Ky = 1.0
• Fy = 50 ksi
Dr. Hasan Katkhuda
Steel Design
Examples (Analysis for Braced Frame)
Dr. Hasan Katkhuda
Steel Design
![Page 15: Chapter 6: Analysis and Design of Beam-Columns · 5 Interaction Formula Pu = Pnt + B2 Plt • Pnt: Axial load assuming that no sidesway occurs (no translation). • Plt :Axial load](https://reader031.vdocument.in/reader031/viewer/2022013006/5af30ef87f8b9a8b4c90f829/html5/thumbnails/15.jpg)
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Examples (Analysis for Braced Frame)
Dr. Hasan Katkhuda
Steel Design
Examples (Analysis for Braced Frame)
Dr. Hasan Katkhuda
Steel Design
![Page 16: Chapter 6: Analysis and Design of Beam-Columns · 5 Interaction Formula Pu = Pnt + B2 Plt • Pnt: Axial load assuming that no sidesway occurs (no translation). • Plt :Axial load](https://reader031.vdocument.in/reader031/viewer/2022013006/5af30ef87f8b9a8b4c90f829/html5/thumbnails/16.jpg)
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Examples (Analysis for Braced Frame)
Dr. Hasan Katkhuda
Steel Design
Design of Beam- Columns
• Because of many variables in the interaction formulas, the design is essentially a trial and error process.
• Amin Mansour Method:
Dr. Hasan Katkhuda
Steel Design
![Page 17: Chapter 6: Analysis and Design of Beam-Columns · 5 Interaction Formula Pu = Pnt + B2 Plt • Pnt: Axial load assuming that no sidesway occurs (no translation). • Plt :Axial load](https://reader031.vdocument.in/reader031/viewer/2022013006/5af30ef87f8b9a8b4c90f829/html5/thumbnails/17.jpg)
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Design of Beam- Columns
Dr. Hasan Katkhuda
Steel Design
Design of Beam- Columns
• Procedure:
Dr. Hasan Katkhuda
Steel Design
![Page 18: Chapter 6: Analysis and Design of Beam-Columns · 5 Interaction Formula Pu = Pnt + B2 Plt • Pnt: Axial load assuming that no sidesway occurs (no translation). • Plt :Axial load](https://reader031.vdocument.in/reader031/viewer/2022013006/5af30ef87f8b9a8b4c90f829/html5/thumbnails/18.jpg)
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Design of Beam- Columns
Dr. Hasan Katkhuda
Steel Design
Design of Beam- Columns
Dr. Hasan Katkhuda
Steel Design
![Page 19: Chapter 6: Analysis and Design of Beam-Columns · 5 Interaction Formula Pu = Pnt + B2 Plt • Pnt: Axial load assuming that no sidesway occurs (no translation). • Plt :Axial load](https://reader031.vdocument.in/reader031/viewer/2022013006/5af30ef87f8b9a8b4c90f829/html5/thumbnails/19.jpg)
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Design of Beam- Columns
Dr. Hasan Katkhuda
Steel Design
Example (Design of Beam- Columns)
• Example 1:
Dr. Hasan Katkhuda
Steel Design
![Page 20: Chapter 6: Analysis and Design of Beam-Columns · 5 Interaction Formula Pu = Pnt + B2 Plt • Pnt: Axial load assuming that no sidesway occurs (no translation). • Plt :Axial load](https://reader031.vdocument.in/reader031/viewer/2022013006/5af30ef87f8b9a8b4c90f829/html5/thumbnails/20.jpg)
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Example (Design of Beam- Columns)
Dr. Hasan Katkhuda
Steel Design
Example (Design of Beam- Columns)
Dr. Hasan Katkhuda
Steel Design
![Page 21: Chapter 6: Analysis and Design of Beam-Columns · 5 Interaction Formula Pu = Pnt + B2 Plt • Pnt: Axial load assuming that no sidesway occurs (no translation). • Plt :Axial load](https://reader031.vdocument.in/reader031/viewer/2022013006/5af30ef87f8b9a8b4c90f829/html5/thumbnails/21.jpg)
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Example (Design of Beam- Columns)
Dr. Hasan Katkhuda
Steel Design
Example (Design of Beam- Columns)
Dr. Hasan Katkhuda
Steel Design
![Page 22: Chapter 6: Analysis and Design of Beam-Columns · 5 Interaction Formula Pu = Pnt + B2 Plt • Pnt: Axial load assuming that no sidesway occurs (no translation). • Plt :Axial load](https://reader031.vdocument.in/reader031/viewer/2022013006/5af30ef87f8b9a8b4c90f829/html5/thumbnails/22.jpg)
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Example (Design of Beam- Columns)
Dr. Hasan Katkhuda
Steel Design
Example (Design of Beam- Columns)
Dr. Hasan Katkhuda
Steel Design