On the Elastic Bending of Columns Due to Dynamic Axial Forces Including Effects of Axial Inertia

Sevin, Eugene

doi:10.1115/1.3643886

Cited by 62 publications

(21 citation statements)

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“…Specifically, shear deformation and rotary inertia effects may be important [68]. In more stocky axially loaded members, some of the thin beam-theory assumptions need to be reexamined.…”

Section: Other Effectsmentioning

confidence: 99%

Continuous Struts

Virgin¹

2007

Vibration of Axially-Loaded Structures

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In this chapter, we consider the dynamics of a thin elastic strut including axial effects, arising primarily from one of two situations:• the axial load is applied externally (including postbuckling), or • deformation is sufficient to cause coupling between axial and bending behavior (the membrane effect).In the first section, attention is focused on a traditional approach to setting up the equations of motion (by means of D'Alembert's principle) for the simple case based on engineering beam theory (Euler-Bernoulli) with the addition of axial loads. The resulting partial differential equation of motion is then separated into temporal and spatial ordinary differential equations and the response analyzed for various magnitudes of the axial load [1,2]. Then an energy approach is used together with Rayleigh's method [3]. In this case, additional terms are retained in the potential energy to allow postbuckled effects to be analyzed [4] and the effect of initial geometric imperfections are included. An alternative approach is developed based on a simple application of Hamilton's principle, and in this instance stretching effects are also included and a solution developed by use of Galerkin's method. This approach will be similar to that used in the previous chapter on strings but now bending strain energy enters into the analysis (as well as compressive axial loading). In the final part of the chapter we consider the dynamics of struts that are loaded by gravity through self-weight. The next chapter will then continue the study of axially loaded members but with the scope opened to include a wider class of problem. Basic FormulationIn this section, we develop the governing equation of motion for a thin, elastic, prismatic beam subject to a constant axial force. In Fig. 7.1(a) a schematic of the beam is shown. It has mass per unit length m, constant flexural rigidity EI, and is subject to an axial load P. The length is L, the coordinate along the beam is x, and the lateral (transverse) deflection is w(x, t). In part (b) is shown an element of the beam between locations x and x + x, which is subject to the D'Alembert forces R(x, t) = m∂ 2 w/∂t 2 . (7.1) 111Cambridge Books Online

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“…Specifically, shear deformation and rotary inertia effects may be important [68]. In more stocky axially loaded members, some of the thin beam-theory assumptions need to be reexamined.…”

Section: Other Effectsmentioning

confidence: 99%

Continuous Struts

Virgin¹

2007

Vibration of Axially-Loaded Structures

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“…We conclude this chapter by considering an axially loaded column in which the end load is applied suddenly [1,2,[38][39][40][41]. We conclude this chapter by considering an axially loaded column in which the end load is applied suddenly [1,2,[38][39][40][41].…”

Section: Snap-through Of a Curved Panelmentioning

confidence: 99%

Suddenly Applied Loads

Virgin¹

2007

Vibration of Axially-Loaded Structures

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“…[2]. Many analytical and experimental studies on the dynamic buckling of a column have been performed since then [3][4][5][6][7][8][9][10][11][12][13][14][15]. In most studies, the effects of the axial stress wave propagation is unaccounted for by assuming that the strain distribution along the column length is uniform after the impact event, a situation that arises at a later time after the initiation of impact.…”

Section: Introductionmentioning

confidence: 99%

The Temporal Evolution of Buckling in a Dynamically Impacted Column

Ji¹,

Waas

2012

Journal of Applied Mechanics

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The time-dependent progressive evolution of transverse displacements of an axially impacted, slender, geometrically imperfect, column is studied here. The analysis is concerned with evaluating the time-histoiy associated with the evolution of the buckling response as a function of the initial geometric imperfection amplitude. The exact solution of the axial stress wave propagation is employed to study the physics of the buckling response with the nonuniform axial strain distribution varying in time and space. The responses of axially impacted columns are examined in light of past experimental results and associated numerical solutions. Results in the present paper are limited to elastic column behavior.

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On the Elastic Bending of Columns Due to Dynamic Axial Forces Including Effects of Axial Inertia

Cited by 62 publications

References 0 publications

Continuous Struts

Continuous Struts

Suddenly Applied Loads

The Temporal Evolution of Buckling in a Dynamically Impacted Column

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