Question

6. The critical stress on a column for elastic buckling given by euler's formula, is

Answer 1

F = n π2 E I / L2    

where

F = allowable load (lb, N)

n = factor accounting for the end conditions

E = modulus of elasticity (lb/in2, Pa (N/m2))

L = length of column (in, m)

I = moment of inertia (in4, m4)

Answer 2

Answer:

The critical stress on a column for elastic buckling given by euler's formula, is P cr = π^2 ⋅ E ⋅ I /  L^2

Explanation:

The Euler column formula predicts the critical buckling load of a long column with pinned ends. The Euler formula is

P cr = π^2 ⋅ E ⋅ I /  L^2

where

E is the modulus of elasticity in (force/length2),

I is the moment of inertia (length4),

L is the length of the column.

These are the following assumptions that are made in Euler's column theory:

• The column is initially straight and load is applied axially

• The cross-section of the column is uniform throughout its length

• The column material is perfectly elastic, homogeneous and isotropic and obeys Hooke's law

• The length of the column is very large as compared to its lateral dimensions

· The direct stress is very small as compared to the bending stress

• The column will fail by buckling alone

• The self-weight of the column is negligible

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