solid Mechanics Rankine's Formula for Column.pptx

column analysis

1. Sub- Solid Mechanics Axially and Eccentrically Loaded Columns Lect. 4 Rankine’s Formula Sanjivani Rural Education Society’s Sanjivani College of Engineering, Kopargaon-423603 An Autonomous Institute, Affiliated to Savitribai Phule Pune University, Pune ISO 9001:2015 Certified, Approved by AICTE, Accredited by NAAC (A Grade) & NBA Department of Civil Engineering Prepared by : Dr. Ghumare S. M. Asso Professor, Civil Engg . Department

2. Rankine’s Formula to find the Buckling or Crippling load Rankine’s Formula: Rankine’s formula is used for short as well as for long columns where slenderness ratio is grater than 80. It considers stress due to compressive load as well as buckling (bending).

3. Rankine’s Formula

4. Rankine’s Formula

5. Rankine’s Constant (a) Sr.No. Materials 6c ( mpa ) Rankine's, Constant ( a or ) 1 Mild Steel 320 1/7500 2 Cast Iron 550 1/1600 3 Wrought Iron 250 1/9000 4 Timber 40 1/750

6. Numerical on Rankine’s formula

7. Problem 1: A column section having external dia. 200mm and thickness 20mm is used as column. The length of column is 4.5m. It is fixed at both ends. Find the safe load using Rankine’s formula. F.O.S.= 4. Take 6c=550mpa & a= 1/1600 Given, D=200mm, t=20mm, 6c=550mpa, P=60KN=60x10 3 N, L=4.5m=4500mm, F.O.S .= 4, a= 1/1600, P R =????

8. Problem 1 Continue……

9. Problem 2: A Strut of length 2m is made of Aluminium tube that has 32mm outer dia. and 4mm wall thickness. Use FOS=2, a=1/7500 & 6c=550mpa. Determine load for following conditions. 1) When both ends fixed 2) Both ends Hinged. Given, L = 2m = 2000mm, d=32mm, d= 24mm, FOS=2, a=1/7500 , 6c=550mpa. P R =??? Case: I- Both Ends Fixed Eff. Length, L e= L /2 =1000mm,

10. Problem 2 Continue……

11. Problem 2 Continue……

12. Problem 3: Compare the Crippling load given by Euler’s formula & Rankine’s formula for circular c/s of 40mm outer dia. and 2m length. Take, a=1/7500, Yield stress 6c=300mpa and E=200Gpa. Assume b oth ends Hinged. Given, D=40mm, a=1/7500 , P R =???, Yield stress 6c=300mpa Both Ends Hinged, Eff. Length, L e= L =2000mm , E=200Gpa.

13. Problem 3 Continue……

14. Problem 4: A hollow cast iron column whose outside diameter is 250mm and 15mm thickness. Column is 4.5m long and fixed at both ends. Calculate the safe load by Rankine’s Formula when Factor of Safety is 4. Also calculate the slenderness ratio and Rankine’s Crippling load. Take E=94Gpa, a=1/1600 and 6 c=550mpa

15. Next Lecture Eccentrically Loaded Column (Direct and Bending Stresses)

16. Thank You