Solid mechanics learning summary
Download
1 / 20

Solid mechanics Learning summary - PowerPoint PPT Presentation


  • 107 Views
  • Uploaded on

Solid mechanics Learning summary. By the end of this chapter you should have learnt about: Combined loading Yield criteria Deflection of beams Elastic-plastic deformations Elastic instability Shear stresses in beams Thick cylinders Asymmetrical bending Strain energy.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Solid mechanics Learning summary' - beverly-morse


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Solid mechanics learning summary
Solid mechanicsLearning summary

By the end of this chapter you should have learnt about:

  • Combined loading

  • Yield criteria

  • Deflection of beams

  • Elastic-plastic deformations

  • Elastic instability

  • Shear stresses in beams

  • Thick cylinders

  • Asymmetrical bending

  • Strain energy

An Introduction to Mechanical Engineering: Part Two


Solid mechanics learning summary1
Solid mechanicsLearning summary

  • Fatigue

  • Fracture mechanics

  • Thermal stresses.

An Introduction to Mechanical Engineering: Part Two


3 2 combined loading key points
3.2 Combined loading – key points

By the end of this section you should have learnt:

  • the basic use of Mohr’s circle for analysing the general state of plane stress

  • how the effect of combined loads on a component can be analysed by considering each load asinitially having an independent effect

  • how to use the principle of superposition to determine the combined effect of these loads.

An Introduction to Mechanical Engineering: Part Two


3 3 yield criteria key points
3.3 Yield criteria – key points

By the end of this section you should have learnt:

  • the difference between ductile and brittle failure, illustrated by the behaviour of bars subjected touniaxial tension and torsion

  • the meaning of yield stress and proof stress, in uniaxial tension, for a material

  • the Tresca (maximum shear stress) yield criterion and the 2D and 3D diagrammatic representationsof it

  • the von Mises (maximum shear strain energy) yield criterion and the 2D and 3D diagrammatic representations of it.

An Introduction to Mechanical Engineering: Part Two


3 4 deflection of beams key points
3.4 Deflection of beams – key points

By the end of this section you should have learnt:

  • how to derive the differential equation of the elastic line (i.e. deflection curve) of a beam

  • how to solve this equation by successive integration to yield the slope, dy/dx, and the deflection, y, of abeam at any position along its span

  • how to use Macaulay’s method, also called the method of singularities, to solve for beam deflections

  • where there are discontinuities in the bending moment distribution arising from discontinuousloading

An Introduction to Mechanical Engineering: Part Two


3 4 deflection of beams key points1
3.4 Deflection of beams – key points

  • how to use different singularity functions in the bending moment expression for different loadingconditions including point loads, uniformly distributed loads and point bending moments

  • how to use Macaulay’s method for statically indeterminate beam problems.

An Introduction to Mechanical Engineering: Part Two


3 5 elastic plastic deformations key points
3.5 Elastic-plastic deformations – key points

By the end of this section you should have learnt:

  • the shapes of uniaxial stress-strain curves and the elastic–perfectly plastic approximation touniaxial stress-strain curves

  • the kinematic and isotropic material behaviour models used to represent cyclic loading behaviour

  • the elastic-plastic bending of beams and the need to use equilibrium, compatibility and behaviour to solve these types of problems

An Introduction to Mechanical Engineering: Part Two


3 5 elastic plastic deformations key points1
3.5 Elastic-plastic deformations – key points

  • the elastic–plastic torsion of shafts and the need to use equilibrium, compatibility and behaviour to solve these types of problems

  • how to determine residual deformations and residual stresses.

An Introduction to Mechanical Engineering: Part Two


3 6 elastic instability key points
3.6 Elastic instability – key points

By the end of this section you should have learnt:

  • Macaulay’s method for determining beam deflection in situations with axial loading

  • the meanings of and the differences between stable, unstable and neutral equilibria

  • how to determine the buckling loads for ideal struts

  • the effects of eccentric loading, initial curvature and transverse loading on the buckling loads

  • how to include the interaction of yield behaviour with buckling and how to represent this interactiongraphically.

An Introduction to Mechanical Engineering: Part Two


3 7 sheer stresses in beams key points
3.7 Sheer stresses in beams – key points

By the end of this section you should have learnt:

  • that in addition to longitudinal bending stresses, beams also carry transverse shear stresses arisingfrom the vertical shear loads acting within the beam

  • how to derive a general formula, in both integral and discrete form, for evaluating the distributionof shear stresses through a cross section

  • how to determine the distribution of the shear stresses through the thickness in a rectangular,circular and I-section beam

An Introduction to Mechanical Engineering: Part Two


3 7 sheer stresses in beams key points1
3.7 Sheer stresses in beams – key points

  • that we can identify the shape of required pumps by calculating the specific speed without knowingthe size of the pump.

An Introduction to Mechanical Engineering: Part Two


3 8 thick cylinders key points
3.8 Thick cylinders – key points

By the end of this sections you should have learnt:

  • the essential differences between the stress analysis of thin and thick cylinders, leading to anunderstanding of statically determinate and statically indeterminate situations

  • how to derive the equilibrium equations for an element of material in a solid body (e.g. a thickcylinder)

  • the derivation of Lame’s equations

  • how to determine stresses caused by shrink-fitting one cylinder onto another

An Introduction to Mechanical Engineering: Part Two


3 8 thick cylinders key points1
3.8 Thick cylinders – key points

  • how to include ‘inertia’ effects into the thick cylinder equations in order to calculate the stresses in arotating disc.

An Introduction to Mechanical Engineering: Part Two


3 9 asymmetrical bending key points
3.9 Asymmetrical bending – key points

By the end of this section you should have learnt:

  • that an asymmetric cross section, in addition to its second moments of area about the x- and y- axes, Ix and Iy, possesses a geometric quantity called the product moment of area, Ixy, with respect tothese axes

  • how to calculate the second moments of area and the product moment of area about aconvenient set of axes

An Introduction to Mechanical Engineering: Part Two


3 9 asymmetrical bending key points1
3.9 Asymmetrical bending – key points

  • that an asymmetric section will have a set of axes at some orientation for which the product moment ofarea is zero and that these axes are called the principal axes

  • that the second moments of area about the principal axes are called the principal second moments ofarea

  • how to determine the second moments of area and the product moment of area about anyoriented set of axes, including the principal axes, using a Mohr’s circle construction

An Introduction to Mechanical Engineering: Part Two


3 9 asymmetrical bending key points2
3.9 Asymmetrical bending – key points

  • that it is convenient to analyse the bending of a beam with an asymmetric section by resolving bendingmoments onto the principal axes of the section

  • how to follow a basic procedure for analysing the bending of a beam with an asymmetric cross section.

An Introduction to Mechanical Engineering: Part Two


3 10 strain energy key points
3.10 Strain energy – key points

By the end of this section you should have learnt:

  • the basic concept of strain energy stored in an elastic body under loading

  • how to calculate strain energy in a body/structure arising from various types of loading, includingtension/compression, bending and torsion

  • Castigliano’s theorem for linear elastic bodies, which enables the deflection or rotation of a body ata point to be calculated from strain energy expression.

An Introduction to Mechanical Engineering: Part Two


3 11 fatigue key points
3.11 Fatigue – key points

By the end of this section you should have learnt:

  • the various stages leading to fatigue failure

  • the basis of the total life and of the damage-tolerant approaches to estimating the number ofcycles to failure

  • how to include the effects of mean and alternating stress on cycles to failure using the Gerber,modified Goodman and Soderberg methods

  • how to include the effect of a stress concentration on fatigue life

  • the S–N design procedure for fatigue life.

An Introduction to Mechanical Engineering: Part Two


3 12 fracture mechanics key points
3.12 Fracture mechanics – key points

By the end of this section you should have learnt:

  • the meaning of linear elastic fracture mechanics (LEFM)

  • what the three crack tip loading modes are

  • the energy and stress intensity factor (Westergaard crack tip stress field) approaches to LEFM

  • the meaning of small-scale yielding and fracture toughness

  • the Paris equation for fatigue crack growth and the effects of the mean and alternatingcomponents of the stress intensity factor.

An Introduction to Mechanical Engineering: Part Two


3 13 thermal stresses key points
3.13 Thermal stresses – key points

By the end of this section you should be able to:

  • understand the cause of thermal strains and how ‘thermal stresses’ are caused by thermal strains

  • include thermal strains in the generalized Hooke’s Law equations

  • include the temperature distribution within a solid component (e.g. a beam, a disc or a tube) in thesolution procedure for the stress distribution

  • understand that stress/strain equations include thermal strain terms but the equilibrium and compatibility equations are the same whether the component is subjected to thermal loading ornot.

An Introduction to Mechanical Engineering: Part Two