Prefi

41問 • 4ヶ月前

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Is measured from the original neutral surface of the beam to the neutral surface of the deformed beam.

Deflection

The deformations disappear and the structure regains its original shape when the actions causing the deformations are removed.

Elastic Deformations

The permanent deformations of structures.

Inelastic (or Plastic) Deformations

Vary linearly with applied loads.

Linear Elastic Deformations

Involves writing the expression for bending moment divided by flexural rigidity of the beam in terms of the distance x along the axis of the beam and integrating the expression to obtain the equations for the slope and deflection of the elastic curve.

Direct Integration Method

Proves to be the most convenient for computing slopes and deflections.

Direct Integration Method

Convenient to use when M/EI is expressed as a single continuous function of x over the entire length of the beam.

Direct Integration Method

Describes the relationship between the beam's deflection and the applied load.

Bernoulli-Euler Beam Equation

When a beam is subjected to several loads, the slope or deflection can be determined by superimposing (algebraically adding) the slopes or deflections due to each of the loads acting individually on the beam.

Superposition Method

Moment-Area Method id developed by __ in __.

Charles E. Green, 1873

Is constructed by dividing the ordinates of the bending moment diagram by the flexural rigidity El.

M/EI Diagram

More convenient to use for beams with loading discontinuities and the variable El.

Moment-Area Method

The change in slope between the tangents to the elastic curve at any two points is equal to the area under the M/(EI) diagram between the two points, provided that the elastic curve is continuous between the two points.

First Moment-Area Theorem

The tangential deviation in the direction perpendicular to the undeformed axis of the beam of a point on the elastic curve from the tangent to the elastic curve at another point is equal to the moment of the area under the M/(EI) diagram between the two points about the point at which the deviation is desired, provided the curve is continuous between the two points.

Second Moment-Area Theorem

Bends the beam concave upward.

Positive Bending Moment

Bends the beam concave downward.

Negative Bending Moment

Both the slope and the deflection of the beam is zero, the tangent of the elastic curve at this point is in the direction of the undeformed axis.

At Fixed Support

The deflection is zero but the slope may not be zero.

At Hinged or Roller Support

The slopes and deflections at the various points are assumed to be positive in the direction shown in the deflected shape or elastic curve structure.

Intuitive Approach

Is the slope and deflection of a point relative to the tangent to the elastic curve at another point.

Reference Tangent

Used when a beam is subjected to different types of loads, such as combination of distributed and concentrated loads.

Bending Moment Diagram by Parts

Done by constructing the bending moment diagram in parts, that is, separate bending moment for each load.

Bending Moment Diagram by Parts

Conjugate-Beam Method is developed by __ in __.

Otto Mohr, 1868

Uses systematic sign convention; a straightforward application because it does not require sketching the elastic curve of the structure.

Conjugate-Beam Method

Is based on the analogy between the relationships among load, shear, and bending moment and the relationships among M/(EI), slope, and deflection.

Conjugate-Beam Method

Involves computing the slopes and deflection of beams by computing the shears and bending moments in the corresponding conjugate beam.

Conjugate-Beam Method

Is a fictitious beam of the same length as the real beam, but it is externally supported and internally connected.

Conjugate Beam

Is based on the principle of conservation of energy.

Work Energy (Virtual Work) Method

"In any closed system, energy can never be created or destroyed. It can only be transformed from one form to another or transferred from one system to another."

Law of Conservation of Energy

Is defined as the moment of the couple times the angle through which the couple rotates

Expressions for the Work (W) of Couples

Principle of Virtual Work was introduced by __ in __.

John Bernoulli, 1717

Provides a powerful analytical tool for many problems in structural mechanics.

Principle of Virtual Work

If a rigid body is in equilibrium under a system of forces and if it is subjected to any small virtual rigid-body displacement, the virtual work done by the external forces is zero.

Principle of Virtual Displacements for Rigid Bodies

The work performed by the forces acting on the structure, as the structure undergoes the virtual displacement from its initial equilibrium position to virtual displaced position.

Virtual Work

The sum of virtual work, W vx and W vy done during the translations in the x and y directions respectivelyand virtual work W vr done during the rotation.

Total Virtual Work

Means imaginary, not real.

Virtual

If a deformable body is in equilibrium under a virtual system of forces (and couples) and if it is subjected to any small real deformation consistent with the support and continuity conditions of the structure.

Principle of Virtual Forces for Deformable Bodies

Is associated with the forces to indicate that the force system is arbitrary and does not depend on the action causing the real deformation.

Virtual

Is based on the principle of virtual forces for deformable bodies as expressed by: virtual external work (Wve) = virtual internal work (Wvi)

Method of Virtual Work

Employs two separate systems: a virtual force system and the real system of loads that cause the deformation to be determined.

Method of Virtual Work

Used if a structure consists of segments with constant El, and is subjected to simple loading.

Graphical Evaluation of Virtual Work Integrals

Enumeration

Sabrina Mikhaela Canindo · 42問 · 1年前

Enumeration