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10 columns

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Mohamed Yaser
Mohamed Yaser

1) The document discusses the stability and buckling behavior of columns under axial loading. It introduces Euler's formula for determining the critical buckling load of pin-ended beams and describes how this analysis can be extended to columns. 2) Sample problems demonstrate how to design columns for centric and eccentric axial loads using these analytical methods and by considering stress limits. Design approaches vary based on the column's slenderness ratio. 3) The effects of eccentric loading are evaluated using a secant formula approach, where the eccentric load is modeled as a centric load plus a bending moment. Stress limits and interaction equations are provided.

TechnologyHealth & Medicine
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10 Columns
Columns Stability of Structures Euler’s Formula for Pin-Ended Beams Extension of Euler’s Formula Sample Problem 10.1 Eccentric Loading; The Secant Formula Sample Problem 10.2 Design of Columns Under Centric Load Sample Problem 10.4 Design of Columns Under an Eccentric Load
Stability of Structures ,[object Object],[object Object],[object Object],[object Object]
Stability of Structures ,[object Object],[object Object]
Stability of Structures ,[object Object],[object Object]
Euler’s Formula for Pin-Ended Beams ,[object Object],[object Object]
Euler’s Formula for Pin-Ended Beams ,[object Object],[object Object]
Extension of Euler’s Formula ,[object Object],[object Object]
Extension of Euler’s Formula
Sample Problem 10.1 An aluminum column of length L and rectangular cross-section has a fixed end at B and supports a centric load at A. Two smooth and rounded fixed plates restrain end A from moving in one of the vertical planes of symmetry but allow it to move in the other plane. ,[object Object],[object Object],L = 20 in. E = 10.1 x 10 6 psi P = 5 kips FS = 2.5
Sample Problem 10.1 ,[object Object],[object Object],[object Object],SOLUTION: The most efficient design occurs when the resistance to buckling is equal in both planes of symmetry. This occurs when the slenderness ratios are equal.
Sample Problem 10.1 L = 20 in. E = 10.1 x 10 6 psi P = 5 kips FS = 2.5 a/b = 0.35 ,[object Object]
Eccentric Loading; The Secant Formula ,[object Object],[object Object],[object Object],[object Object]
Eccentric Loading; The Secant Formula
Sample Problem 10.2 The uniform column consists of an 8-ft section of structural tubing having the cross-section shown. ,[object Object],[object Object]
Sample Problem 10.2 ,[object Object],[object Object],- Effective length, - Critical load, - Allowable load,
Sample Problem 10.2 ,[object Object],- End deflection, - Maximum normal stress,
Design of Columns Under Centric Load ,[object Object],[object Object],[object Object],[object Object],[object Object]
Design of Columns Under Centric Load Structural Steel American Inst. of Steel Construction ,[object Object],[object Object],[object Object]
Design of Columns Under Centric Load Aluminum Aluminum Association, Inc. ,[object Object],L e /r > 66: ,[object Object],L e /r > 66:
Sample Problem 10.4 Using the aluminum alloy2014-T6, determine the smallest diameter rod which can be used to support the centric load P = 60 kN if a) L = 750 mm, b) L = 300 mm ,[object Object],[object Object],[object Object],[object Object]
Sample Problem 10.4 ,[object Object],[object Object],[object Object],assumption was correct
Sample Problem 10.4 ,[object Object],[object Object],[object Object],assumption was correct
Design of Columns Under an Eccentric Load ,[object Object],[object Object],[object Object],[object Object]

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  • 2. Columns Stability of Structures Euler’s Formula for Pin-Ended Beams Extension of Euler’s Formula Sample Problem 10.1 Eccentric Loading; The Secant Formula Sample Problem 10.2 Design of Columns Under Centric Load Sample Problem 10.4 Design of Columns Under an Eccentric Load
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