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BUCKLING OF COLUMN WHEN ONE END HINGED AND ONE END FIXED AIM:
To final buckling load of column using column test setup arrangement under one end hinged and one end fixed .
EULER’S COLUMN THEORY: As per Euler’s equation for buckling load of long column based on bending stress, the effect of direct stress is neglected. This may be justified with the statement; the direct stress induced in a long column is negligible as compared to the bending stress. General Euler’s equation
π2 EI ρ = ---------- ℓ2
ρ Crippling load E Young’s modulus I moment of inertia ℓ Actual length (varies with end conditions) THEORY:Euler’s column theory deals with perfect columns only. I.e. columns with no imperfections. In practice, no column is perfect. Imperfections always exist in column and may manifest in anyone of the following ways 1. The column column is not not initially initially straight. straight. It is curved initiall initially. y.
2. The column column materia materiall behavior behavior may may not be be perfectly perfectly linear. linear. The column is not slender. It may be short, thick column
1
ASSUMPTION: • Initially the column is perfectly straight and the load applied is truly axial. • The cross section of column is uniform throughout its length. • The column material is perfectly elastic homogenous and isotropic and they Obey’s Hooks law. • The length of column is very large as compared to its cross-sectional dimensional and the failure occurs due to buckling load. PROCEDURE: • Consider a column AB of length ‘ ℓ’ with one end fixed other end hinged. • The column cannot be rotated because it is one end fixed end and other end hinged. • It is positioned to have a complete supports. • The load is gradually applied by rotating the loading wheel connected to load cell intern to the digital meter. • The load indicator is connected with column test setup. • The load indicator is viewed simultaneously from the display of digital load indicator. • Now the column just starts buckling. • Till the column deflection of column occurs as shown in fig. meanwhile applied load value approximately coincides with the theoretical value. MODEL CALCULATION : (ONE END FIXED AND OTHERS ENDS ARE HINGED)
