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Chapter 5 Introduction to Axially Loaded Compression Members.

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Presentation on theme: "Chapter 5 Introduction to Axially Loaded Compression Members."— Presentation transcript:

1 Chapter 5 Introduction to Axially Loaded Compression Members

2 2 Compression Members ColumnsChords of TrussesBracing Members Columns are straight vertical members whose lengths are considerably greater than their thicknesses

3 Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012 3 Residual Stresses The stresses that remain in a material after the original cause of the stresses, such as external forces, heat gradient, has been removed. Caused by : Uneven cooling of hot rolled sections Uneven cooling welded materials Cambering Affect strength Could be 10 to 15 ksi or more

4 Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012 4

5 5 Column Failure Modes Flexural Buckling (Euler buckling) Local BucklingTorsional Buckling

6 6 Euler Buckling depends on Length, L Material, E Cross section, A or I or r End support condition

7 Columns are Long and slender members subjected to an axial compressive force. Buckling is Lateral deflection of columns Buckling result in instability of columns, and causes sudden failure. Buckling occurs when load P > P cr the critical load

8 Column with Pin Support (Ideal) Ideal column : Linear-Elastic Homogeneous material P is applied thru c.g. perfectly straight before loading The flexural differential equation

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10 Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012 10 Buckling Load of an elastic column is calculated using Euler Formula Dividing both sides by cross sectional area A

11 11 Column Strength Curve

12 Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012 12

13 Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012 13 End restraint and Effective Lengths of Columns K is the Effective Length Factor KL is the Effective Length of Column

14 Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012 14

15 Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012 15

16 Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012 16 The strength of long columns is predicted by Euler formula (elastic buckling control) For short columns, the failure stress will equal the yield stress. For intermediate columns, the member will fail by both yielding and buckling.

17 Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012 17

18 18

19 AISCM 14 th Edition19

20 AISCM 14 th Edition20

21 AISCM 14 th Edition21

22 AISCM 14 th Edition22

23 AISCM 14 th Edition23

24 Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012 24 Stiffened Elements Unstiffened Elements

25 Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012 25 Limiting values for the width thickness ratio AISCS section B4 and Table B4.1a of AISCS Control of Local Buckling

26 Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012 26

27 Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012 27

28 Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012 28

29 Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012 29

30 Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012 30

31 Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012 31

32 Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012 32

33 Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012 33

34 Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012 34

35 Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012 35

36 Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012 36

37 Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012 37

38 Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012 38

39 Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012 39

40 Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012 40

41 Structural Steel Design by McCormac and Csernak, 5th Edition, Int. 2012 41 HW # 4 : Problems 5-3 and 5-8


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