This preview shows pages 1–3. Sign up to view the full content.
Useful solutions
to
standard
problems
in
Introduction
and
synopsis
Modelling
is a key part of design. In the early stage, approximate modelling establishes whether
the concept will work at all, and identifies the combination of material properties which maximize
performance. At the embodiment stage, more accurate modelling brackets values for the forces, the
displacements, the velocities, the heat fluxes and the dimensions of the components. And in the final
stage, modelling gives precise values for stresses, strains and failure probability in key components;
power, speed, efficiency and so forth.
Many components with simple geometries and loads have been modelled already. Many more
complex components can be modelled approximately by idealizing them as one of these. There is no
need to reinvent the beam or the column or the pressure vessel; their behaviour under all common
types of loading has already been analysed. The important thing is to know that the results exist
and where to find them.
This appendix summarizes the results of modelling a number of standard problems. Their useful
ness cannot be overstated. Many problems of conceptual design can be treated, with adequate
precision, by patching together the solutions given here; and even the detailed analysis of non
critical components can often be tackled in the same way. Even when this approximate approach
is not sufficiently accurate, the insight it gives is valuable.
The appendix contains 15 double page sections which list, with a short commentary, results for
constitutive equations; for the loading of beams, columns and torsion bars; for contact stresses,
cracks and other stress concentrations; for pressure vessels, vibrating beams and plates; and for the
flow of heat and matter. They are drawn from numerous sources, listed under Further reading in
Section A.16.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document376
Materials
Selection in
Mechanical
Design
A.l
Constitutive equations for mechanical response
The behaviour of a component when it is loaded depends on the
mechanism
by which it deforms.
A
beam loaded in bending may deflect elastically; it may yield plastically; it may deform by creep;
and it may fracture in a brittle or in a ductile way. The equation which describes the material
response is known as a
constitutive equation.
Each mechanism is characterized by a different
constitutive equation. The constitutive equation contains one or more than one
material property
:
Young’s modulus,
E,
and Poisson’s ratio,
II,
are the material properties which enter the constitutive
equation for linearelastic deformation; the yield strength,
uy,
is the material property which enters
the constitutive equation for plastic flow; creep constants,
EO,
a0
and
n
enter the equation for
creep; the fracture toughness,
IC[,,
enters that for brittle fracture.
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '08
 SIDDHARTHAN

Click to edit the document details