Stress Analysis Flashcards

Question

What is torsional stress? | What is pure torsion?

Answer 1

Twisting due to application of a moment A circular bar is in pure torsion when its cross section retains its shape (i.e. remains circular and the radius is unchanged)

Answer 2

Deformation is zero at the central axis (line longitudinally through the bar), and is maximal at the outer surface The angle of twist, and hence the shear stress and shear strain also increase towards the surface of the bar

Answer 3

tau = (Gθr(AB)) / L ``` τ = shear stress G = modulus of rigidity θ = angle of twist (rad) r(AB) = radius of bar L = length of bar ```

Answer 4

ϕ = θr(AB) / L ``` ϕ = shear strain θ = angle of twist (rad) r(AB) = radius of bar L = length of bar ```

Answer 5

Since the deformation in the middle is zero, and therefore the stress and strain, the material is effectively redundant Most of the deformation and stress occurs at the outer surface, therefore using a hollow bar will help save material, and increase the strength-to-weight ratio of the bar, as found in bones

Answer 6

A measure of the distribution of the material about the central axis Unit = m^4

Answer 7

M = JGθ/L ``` M = twisting moment J = polar second moment of area θ = angle of twist (rad) L = Length of bar ```

Answer 8

M/J = τ/R = Gθ/L ``` M = twisting moment J = polar second moment of area τ = shear stress R = radius of cross-section G = modulus of rigidity θ = angle of twist (rad) L = length of bar ```

Answer 9

J = πd^4/32

Answer 10

J = π(D^4 - d^4)/32 ``` D = outer diameter d = inner diameter ```

Answer 11

The distal polar second moment of area is smaller than the proximal polar second moment of area

Answer 12

During reciprocal gait, loadings on the hip during the stance phase produce a tensile load on the superior aspect of the femoral neck, and compressive load on the inferior aspect The gluteus medius, located superiorly to the femoral neck, contracts to pull up the superior aspect, therefore also bringing it into compression. This effectively neutralises the tensile stress.

Answer 13

Devices used to measure the strain, and consequently the stress, at the surface of a structure It consists of a very thin metal foil locate between 2 pieces of thin insulating film. In use, the gauge is cemented to the surface of the material where it is required to measure the strain. As the material changes in dimension, the length of the gauge will also, altering the electrical resistance of the foil. The change is proportional to the strain and may be measured using an electronic circuit. They can be applied to the actual structure under study, there is no need to build an experimental model. They are ideal for measuring strain in a few directions at a few specific locations, however are not really practical when an investigation of a complex structure is needed.

Answer 14

An experimental technique for stress analysis which is useful for complex geometrical structures with complicated loadings, which are usually transparent e.g. certain plastics When transparent materials are subjected to force, some of their optical properties change in direct proportion to the stresses developed. The material becomes birefringent and a colourful interference pattern is observed. Polarised light passing through the stressed material splits into 2 beams, creating a fringe pattern, which can be used to quantify and localise stress. The closed the fringes, the steeper the stress gradient, indicating an area of stress concentration It is also possible to coat a structure in a special photo elastic resin, in this way the stress present at the surface can be quantified

Answer 15

A computing tool which creates a mathematical model of a structure and the applied loads to simulate the stress which would occur in real life A large number of simplified problems are substituted for one very complex one. The structure is split up into several small sub-regions called elements, and assoc w each element are a number of points called nodes. The system generates a series of equations for each node, of which there may be tens of thousands. Certain assumptions can be made about the initial value of some of these nodes, which will allow the remainder of the equations to be solved. It produces an illustration with arrows and colours. The arrows represent the point of application and direction of applied forces. Blue colour = compression, red colour = tension