Assumptions made in Eulers theory is/are -(i) The column is initially straight(ii) The cross-section is uniform throughout(iii) The line of thrust coincides exactly with the axis of the column(iv) The material is homogeneous but not isotropic(v) The shortening of the column due to axial compression is negligiblea)(i), (ii), (iii) andamp; (iv)b)(i), (ii), (iii) andamp; (v)c)(ii) andamp; (iii) onlyd)All of the aboveCorrect answer is option 'B'. Can you explain this answer?

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Assumptions made in Euler's theory is/are -
(i) The column is initially straight
(ii) The cross-section is uniform throughout
(iii) The line of thrust coincides exactly with the axis of the column
(iv) The material is homogeneous but not isotropic
(v) The shortening of the column due to axial compression is negligible

a)
(i), (ii), (iii) & (iv)
b)
(i), (ii), (iii) & (v)
c)
(ii) & (iii) only
d)
All of the above

Correct answer is option 'B'. Can you explain this answer?

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Assumptions made in Eulers theory is/are -(i) The column is initially ...

Euler’s theory:

It gives the buckling load for the column (compression member).

The following are the assumptions made in this theory:

The column is very long in proportion to its cross-sectional dimensions.
The column is initially straight and the compressive load is applied axially.
The material of the column is elastic, homogeneous, and isotropic.
The effect of direct stress is very small in comparison with bending stress.
Column shall fail by buckling alone.
The effect of the self-weight of the column is negligible.
The cross-section is uniform.
The shortening of the column due to axial compression is negligible.
The line of thrust coincides exactly with the axis of the column.

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Assumptions made in Eulers theory is/are -(i) The column is initially ...

Assumptions made in Euler's theory:
Assumptions play a crucial role in simplifying the analysis of complex structures. In Euler's theory for column buckling, the following assumptions are made:

(i) The column is initially straight:
- This assumption simplifies the analysis by assuming that the column is perfectly straight before any external forces are applied.

(ii) The cross-section is uniform throughout:
- Assuming a uniform cross-section helps in simplifying the calculations and analysis of the column behavior under compressive loads.

(iii) The line of thrust coincides exactly with the axis of the column:
- This assumption simplifies the analysis by assuming that the compressive force is applied along the central axis of the column.

(v) The material is homogeneous but not isotropic:
- Homogeneity assumes that the material properties are uniform throughout the column, while the non-isotropic assumption implies that the material properties may vary along different directions.

(v) The shortening of the column due to axial compression is negligible:
- Neglecting the shortening of the column simplifies the analysis by assuming that the deformation due to compressive loads is primarily in the form of buckling rather than axial shortening.
Therefore, the correct answer is option B, which includes assumptions (i), (ii), (iii), and (v) in Euler's theory for column buckling.

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Assumptions made in Eulers theory is/are -(i) The column is initially straight(ii) The cross-section is uniform throughout(iii) The line of thrust coincides exactly with the axis of the column(iv) The material is homogeneous but not isotropic(v) The shortening of the column due to axial compression is negligiblea)(i), (ii), (iii) & (iv)b)(i), (ii), (iii) & (v)c)(ii) & (iii) onlyd)All of the aboveCorrect answer is option 'B'. Can you explain this answer?

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