Design of Columns
Transcript of Design of Columns
![Page 1: Design of Columns](https://reader035.fdocuments.in/reader035/viewer/2022082203/577c7ddb1a28abe0549ff73d/html5/thumbnails/1.jpg)
Design of Columns
![Page 2: Design of Columns](https://reader035.fdocuments.in/reader035/viewer/2022082203/577c7ddb1a28abe0549ff73d/html5/thumbnails/2.jpg)
Design of Columns
Column- a member loaded in compression such that either its length or eccentric loading causes it to experience more than pure compression
Can be classified as
a. Long columns
b. Short Columns
![Page 3: Design of Columns](https://reader035.fdocuments.in/reader035/viewer/2022082203/577c7ddb1a28abe0549ff73d/html5/thumbnails/3.jpg)
Design of Columns
Long columns- fail due to structurally(buckling or elasticity failure)
Short columns- fail to materially (yielding failure)
When P reaches critical load, column becomes unstable and bending develops rapidly
Critical load depends on end conditions
![Page 4: Design of Columns](https://reader035.fdocuments.in/reader035/viewer/2022082203/577c7ddb1a28abe0549ff73d/html5/thumbnails/4.jpg)
Design of Columns
Parameters needed in determining the type of column
Radius of Gyration,r: 𝑟 =𝐼
𝐴
Effective Length,Le: 𝐿𝑒 =𝐿
𝐶,where C=End Condition Constant
Slenderness Ratio,λ:𝜆 =𝐿𝑒
𝑟
![Page 5: Design of Columns](https://reader035.fdocuments.in/reader035/viewer/2022082203/577c7ddb1a28abe0549ff73d/html5/thumbnails/5.jpg)
Design of ColumnsEnd Conditions and Effective Length of Columns
C=1/4 C=1 C=2 C=4 C=1
![Page 6: Design of Columns](https://reader035.fdocuments.in/reader035/viewer/2022082203/577c7ddb1a28abe0549ff73d/html5/thumbnails/6.jpg)
Design of Columns
Compare 𝐿𝑒
𝑟with
2𝜋2𝐶𝐸
𝑆𝑦
1
2
if 𝐿𝑒
𝑟>
2𝜋2𝐶𝐸
𝑆𝑦
1
2, long columns, use Euler’s Formula
if 𝐿𝑒
𝑟<
2𝜋2𝐶𝐸
𝑆𝑦
1
2, short columns, use J.B. Johnson’s Formula
![Page 7: Design of Columns](https://reader035.fdocuments.in/reader035/viewer/2022082203/577c7ddb1a28abe0549ff73d/html5/thumbnails/7.jpg)
Design of Columns
Central Loading:
Euler’s Formula:
J.B. Johnson’s Formula:
Factor of safety:
Where P=maximum allowable load𝑃𝑐𝑟 = 𝑁𝑃
![Page 8: Design of Columns](https://reader035.fdocuments.in/reader035/viewer/2022082203/577c7ddb1a28abe0549ff73d/html5/thumbnails/8.jpg)
Design of Columns
Eccentric Loading: For both ColumnsMaximum deflection:
Factor of safety:Where P=maximum allowable load e=eccentricity, c=distnace of NA to extreme fiber
𝜎𝑚𝑎𝑥 = 𝜎𝑐𝑟 =𝑃𝑐𝑟𝐴
1 +𝑒𝑐
𝑟2𝑠𝑒𝑐
1
2
𝑃𝑐𝑟𝐸𝐴
𝐿𝑒𝑟
𝑃𝑐𝑟 = 𝑁𝑃
![Page 9: Design of Columns](https://reader035.fdocuments.in/reader035/viewer/2022082203/577c7ddb1a28abe0549ff73d/html5/thumbnails/9.jpg)
Design of Columns
Develop a specific Euler’s and J.B. Johnson’s Eqautions for the sizes of columns having
a) Round cross sections, diameter d is required
b) Rectangular cross section, h<b, base b is required
![Page 10: Design of Columns](https://reader035.fdocuments.in/reader035/viewer/2022082203/577c7ddb1a28abe0549ff73d/html5/thumbnails/10.jpg)
Design of Columns
Specify the diameter of a round column 1.5m long that is to carry a maximum load estimated to be 22kN. Use a design factor of 4 and consider the ends as pinned rounded. The column material selected has a minimum yiled strength of 500 Mpa at a modulus of elasticity of 207 Gpa.
![Page 11: Design of Columns](https://reader035.fdocuments.in/reader035/viewer/2022082203/577c7ddb1a28abe0549ff73d/html5/thumbnails/11.jpg)
Design of Columns
A round steel rod made of structural steel,with yield strength of 48ksi and E=30Mpsi, is to be used as a column, centrally loaded with 10 kips; N = 3 . Determine the diameter for L = 25 in.
![Page 12: Design of Columns](https://reader035.fdocuments.in/reader035/viewer/2022082203/577c7ddb1a28abe0549ff73d/html5/thumbnails/12.jpg)
Design of Columns
The column above is subjected to an axial compressive load of 15 kips. Made of AISI C1030, as rolled(Sy=51 ksi and E=30Mpsi), it has sectional length of 20 in. Assume a loose fit with the pins. What is
a. the critical load for this column
b. the design factor
c. the equivalent stress under a load of 15 kips
d. Maximum stress for the foregoing load, when eccentricity ratio=0.25 and eccentricity is Le/400