Columns, Strain Energy & Applications Explore how materials behave under compression, energy storage, and real-world loading conditions — crucial for understanding structures, springs, and machine elements. 1 / 20 The strain energy stored in a body under shear stress τ is τ²/2G τ²/G Gτ²/2 τG² 2 / 20 The deflection of a spring is directly proportional to Spring diameter Load applied Pitch Coil number According to Hooke’s law, F=kx → deflection (x) ∝ load (F) for elastic springs. 3 / 20 The toughness of a material measures Plasticity Hardness Elasticity Energy absorbed till fracture Toughness = area under stress-strain curve → represents total energy absorbed before failure. 4 / 20 The resilience of a material measures Energy absorbed before elastic limit Energy at fracture Elasticity Hardness Resilience is the ability to absorb energy within elastic limit — important for materials under impact loads like springs. 5 / 20 The area under a load–deflection curve represents Work done Strain Stress Modulus The area under the load–deflection graph gives total work done by the load, part of which is stored as strain energy. 6 / 20 The column with both ends fixed has effective length L L/2 2L √2L For both ends fixed, effective length Le=L/2. The fixing at both ends increases stability. 7 / 20 The unit of strain energy is Joule N/m² N Watt Since strain energy is a form of energy, its SI unit is Joule (J). 8 / 20 A beam stores maximum strain energy when it is Simply supported Cantilevered Fixed Hinged Fixed beams resist rotation and deflection, storing more strain energy under the same load compared to other supports. 9 / 20 In a column, buckling occurs due to Axial compression Transverse shear Torsion Bending moment Buckling happens when compressive axial load causes lateral instability, even if stress is below the material’s yield point. 10 / 20 The impact load produces Less stress Same stress More stress No stress Impact loading produces higher stresses because the load acts quickly and generates additional kinetic energy 11 / 20 A suddenly applied load produces stress Twice the gradually applied load Same as gradually applied load Half the gradually applied load Depends on area Sudden loads cause dynamic stress twice that of gradually applied static loads, as energy is absorbed instantaneously. strain energy varies with the square of the applied stress and the material’s volume. 12 / 20 The total strain energy stored in a bar is proportional to Area Stress Length Stress² 13 / 20 The strain energy per unit volume is σ/E ½ σ²/E σ²/E Eσ² 14 / 20 Rankine’s formula is used to determine Bending stress Critical load Deflection Torsion 15 / 20 The radius of gyration is defined as I/A A/I L/I √(I/A) 16 / 20 The slenderness ratio is given by L/r r/L L²/r r²/L 17 / 20 The effective length of a column hinged at one end and fixed at the other is L/2 √2L L/√2 0.7L Effective length Le=0.7L for a column with one end fixed and the other hinged, as per Euler’s conditions. 18 / 20 The Euler’s crippling load for a column hinged at both ends is π²EI/L² 4π²EI/L² π²EI/4L² 2π²EI/L² 19 / 20 Euler’s buckling load formula is valid for Short columns Long columns All columns Rectangular bars Euler’s theory assumes elastic buckling and is valid only for long, slender columns where failure occurs by buckling, not by crushing. 20 / 20 The load at which a slender column just begins to buckle is called Critical load Yield load Safe load Ultimate load Critical (Euler’s) load is the load that causes sudden lateral deflection (buckling) in a long column before material failure. Your score isThe average score is 0% 0% Restart quiz
