Mechanical Engineering - Strength of Materials - Discussion
Discussion Forum : Strength of Materials - Section 1 (Q.No. 4)
4.
Euler's formula holds good only for
Discussion:
49 comments Page 1 of 5.
Pradeep sai siva aremanda said:
1 decade ago
Euler's formulae is meant to calculate critical load(the load at which column bends(buckling)) of long column's(only).
Euler's formulae for critical load is = ((pi)^2)EI/(le)^2.
Where 'le' is equivalent length based on boundary conditions of column
IF both ends of column are hinged le=l.
fixed le=l/2.
If one is fixed and other end is free then le=2l.
If one end is fixed other end is hinged then le=l/(2)^1/2.
Euler's formulae for critical load is = ((pi)^2)EI/(le)^2.
Where 'le' is equivalent length based on boundary conditions of column
IF both ends of column are hinged le=l.
fixed le=l/2.
If one is fixed and other end is free then le=2l.
If one end is fixed other end is hinged then le=l/(2)^1/2.
Sozharajan said:
8 years ago
Length of the column is greater than 30 times its diameter is called long column, its fail only due to buckling but not crushing. Euler's formula only applicable for bukling si lit applicable for long column, if the length of column less than, 8times of its diameter is called short column, it will be subjected to crushing and buckling. Rankine formula suitable for this.
(2)
Korra naresh said:
9 years ago
The assumption of Euler's theory.
1. The column is initially straight.
2. The cross section of the column is uniform.
3. The length of the column is large while comparing to its lateral dimension.
4. Shortening of a column is neglected.
5. The material of column is homogeneous and isotropic and obeys Hooks law.
1. The column is initially straight.
2. The cross section of the column is uniform.
3. The length of the column is large while comparing to its lateral dimension.
4. Shortening of a column is neglected.
5. The material of column is homogeneous and isotropic and obeys Hooks law.
Mayurakshi Salve said:
10 months ago
Euler's formula holds good only for long columns.
It is applicable when a column is slender and its failure is due to buckling, not material strength.
For short columns, failure usually occurs due to compressive stress, not buckling, so Euler's formula is invalid.
It is applicable when a column is slender and its failure is due to buckling, not material strength.
For short columns, failure usually occurs due to compressive stress, not buckling, so Euler's formula is invalid.
Sachin said:
1 decade ago
Euler's formula ie critical stress is inversely proportional to length of column. Hence larger the length lesser will be the defined critical stress. Also applicable only for columns having slenderness ratio (l/k) greater than 80.
Paatel said:
6 years ago
Euler's formula gives the relation between bending and crushing when short columns the bending stress is low as compared to crushing stress. In the long column, the bending and crushing are relatively equal to each other.
(3)
Khekato G said:
3 years ago
Euler's formula gives correct results only for very long columns.
For short or long columns Rankine's Formula is used.
Load columns can be analysed with Euler's column formulas can be given as;
P = n 2 π 2 E I L 2.
For short or long columns Rankine's Formula is used.
Load columns can be analysed with Euler's column formulas can be given as;
P = n 2 π 2 E I L 2.
(10)
NARAYANA H said:
8 years ago
Slenderness ratio is the ratio of effective length to least radius of gyration.
Least radius of gyration is from,
I = Ak^2.
Where, I is least moment of inertia I.e., minimum of Ixx or Iyy.
Least radius of gyration is from,
I = Ak^2.
Where, I is least moment of inertia I.e., minimum of Ixx or Iyy.
K.aravind said:
1 decade ago
Euler has formulated the formula for those columns which fail by both crushing as well as buckling. But short columns fail only by crushing so only long columns obey eulers formula.
Ganesh appu said:
9 years ago
@Hari Hara Krishna.
Critical stress is the ratio of critical load and area. Critical load is the load at which the buckling of the column is initiated.
Critical stress is the ratio of critical load and area. Critical load is the load at which the buckling of the column is initiated.
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