Cos ex pxnp I

Line of action of normal stress By definition the normal stress is that which acts normal to the plane, i.e. the line of action of the normal stress has the same direction cosines as the normal to plane viz I, m and n. 8.4.3. Line of action of shear stress As shown in 8.4 the resultant stress pn can be considered to have two components one normal to the plane (cr ) and one along the plane (the shear stress r ) - see Fig. 8.6. Let the direction cosines of the...

Info

Expanding the force displacement eqn. (9.39) to include terms associated with the y- direction, requires the insertion of zeros in the stiffness matrix of eqn. (9.41) and hence becomes identical to eqn. (9.14). Element stress matrix in local coordinates For the case of a linear rod element, substituting from eqn. (9.35) into eqn. (9.36) gives the element stress as Again, by inserting zeros in the matrix, to accommodate terms associated with the y- direction, eqn. (9.42) becomes identical to...

Introduction To The Finite Element Method

So far in this text we have studied the means by which components can be analysed using so-called Mechanics of Materials approaches whereby, subject to making simplifying assumptions, solutions can be obtained by hand calculation. In the analysis of complex situations such an approach may not yield appropriate or adequate results and calls for other methods. In addition to experimental methods, numerical techniques using digital computers now provide a powerful alternative. Numerical techniques...

La aJcrj ff ii Vax ay J

A similar equation can be obtained for the plane stress case, namely If the body forces X and Y have constant values the same equation holds for both plane stress and plane strain, namely (ar2 + dy2 xx + yy) Vl xx + yy) This equation is known as the Laplace differential equation or the harmonic differential equation. The function (oxx + oyy) is referred to as a harmonic function. It is interesting to note that the Laplace equation, which of course incorporates all the previous equations, does...

P

Where P is the applied load, D is the disc diameter and t is the thickness. Thus, comparing with the photoelastic eqn. (6.1), The slope of the load versus fringe order graph is given by 6.18. Fractional fringe order determination - compensation techniques The accuracy of the photoelastic technique is limited, among other things, to the accuracy with which the fringe order at the point under investigation can be evaluated. It is not sufficiently accurate to count to the nearest whole number of...

Tf

Negative Nominal Strains

To the substrate as a result of which they are usually more stable. Additionally, the grids of foil gauges can be made much smaller and there is almost unlimited freedom of grid configuration, solder tab arrangement, multiple grid configuration, etc. Figure 6.8 shows but a few of the many types and size of gauge which are available. So vast is the available range that it is difficult to foresee any situation for which there is no gauge suitable. Most manufacturers' catalogues'13' give full...

U

Typical residual stress distribution with depth for the shot-peening process. For lower-strength steels and alloys om can initially reach the yield stress or 0.1 proof stress but this will fade under cyclic loading. Cold rolling of threads, crankpins and axles relies on similar principles to those outlined above with, in this case, continuous pressure of the rollers producing controlled amounts of cold working. Further examples of cold working are the bending of pipes and conduits,...

W

Partial Plastic Stress

Other structures may require even more plastic hinges depending on their particular support conditions and degree of redundancy, but these need not be considered here. It should be evident, however, that there is now even more strength or load-carrying capacity available beyond that suggested by the shape factor, i.e. with a knowledge of the yield stress and hence the maximum elastic moment for any particular cross-section, the shape factor determines the increase in moment required to produce...

T Section Structural Material

A cantilever is to be constructed from a 40 mm x 60 mm T-section beam with a uniform thickness of 5 mm. The cantilever is to carry a u.d.l. over its complete length of 1 m. Determine the maximum u.d.l. that the cantilever can carry if yielding is permitted over the lower part of the web to a depth of 10 mm. ay 225 MN m. 3.7 B . A 305 mm x 127 mm symmetrical I-section has flanges 13 mm thick and a web 5.4 mm thick. Treating the web and flanges as rectangles, calculate the bending moment...

Experimental Stress Analysis

We live today in a complex world of manmade structures and machines. We work in buildings which may be many storeys high and travel in cars and ships, trains and planes we build huge bridges and concrete dams and send mammoth rockets into space. Such is our confidence in the modern engineer that we take these manmade structures for granted. We assume that the bridge will not collapse under the weight of the car and that the wings will not fall away from the aircraft. We are confident that the...

Disc With Hole Rotating Radial Displacement

1.1 Product second moment of area 3 1.2 Principal second moments of area 4 1.3 Mohr's circle of second moments of area 6 1.4 Land's circle of second moments of area 7 1.5 Rotation of axes determination of moments of area in terms of the principal values 8 1.6 The ellipse of second moments of area 9 1.8 Stress determination 11 1.9 Alternative procedure for stress determination 11 1.10 Alternative procedure using the momental ellipse 13 1.11 Deflections 15 Examples 16 Problems 24 2.2 Equivalent...

Euler And Rankine-gordon

Euler Curve

Having derived the result for the buckling load of a strut with pinned ends the Euler loads for other end conditions may all be written in the same form, where I is the equivalent length of the strut and can be related to the actual length of the strut depending on the end conditions. The equivalent length is found to be the length of a simple bow half sine-wave in each of the strut deflection curves shown in Fig. 2.6. The buckling load for each end condition shown is then readily obtained. The...