Solve Prob. 10.91 using the interaction method and an allowable stress in bending of 1300 psi.

Name: Problem 92, Chapter 10: Mechanics of Materials
Uploaded: 2021-11-04T06:45:55-08:00
Duration: 4 min 23 s
Channel: Ameer Said
Description: Solve Prob. 10.91 using the interaction method and an allowable stress in bending of 1300 psi.

Solve Prob. 10.91 using the interaction method and an...

Key Concepts

Bending Stress

Bending stress is a measure of the internal stress induced in a beam or other structural member when subjected to bending moments. It is determined by the applied moment, the section geometry (especially the moment of inertia), and the distance from the neutral axis, and is a critical factor in designing safe and efficient members.

Combined Stress Analysis

Combined stress analysis involves evaluating the effects of multiple simultaneous loads, such as bending and axial loads, on a structural member. By superimposing the individual stress contributions and checking their cumulative effect against allowable limits, engineers can ensure that the design maintains sufficient safety margins under complex loading scenarios.

Interaction Method

The interaction method is a design approach used for structural members that are subjected to more than one type of loading simultaneously, such as bending and axial loads. It involves evaluating the combined effect of these loads using interaction formulas or diagrams to ensure that the overall stress does not exceed the material’s capacity.

Allowable Stress

Allowable stress refers to the maximum stress level that the material is permitted to experience under given loading conditions without risk of failure. In design calculations, such a value is used as a safety limit to verify that the member's stresses remain within acceptable bounds throughout its service life.

Transcript

00:01 All right so in this problem we are given that y sub s values at two different temperatures and also 140 mega pascals so and the value of the stress exponent which is in in this stress is exponent value is 8 .5 right and it asks that we to determine that a steady state creep rate at a stress up 483 megapascals right so and also a temperature of 1300 right kelvin so taking the natural lag of both side of the equation so y sub s1 prime this will be a natural log of k2 plus n time natural log of sigma minus q sub c over r t right so with the given data there are two unknowns in this equation which is k s k2 this is unknown and this is k -c unknown right so here using the data provided in the problem statement so we can set up two independent equations right the first equation will be natural lag up 6 .6 times 10 to the power minus 4 para right and this will be be equal to natural lag up k2 plus 8 .5 which is the value of n times natural lag up 140 megapascals minus q sub c which is unknown or 8 .3 joules per mole per kilven right per mole kilven and this is the gas constant in the temperature is 1 ,090 kil1 right so this is the first equation the second equation will be natural log of 8 .8 times 10 to the power minus 2 per hour right and this is natural log of k2 plus 8 .5 natural log of 1 40 mega pascal and minus q sub c which is unknown or 8 .3, 8 .31 times 1 ,200 kil1 right.

02:35 So this is simple linear algebra.

02:38 So solving these equation simultaneously, we will have that, we will point that, that k2 will lead to this will be 57 .5 per hour, and q subc, which is activation energy, which will be, this value right jols per mole right so thus it is now possible to solve power y sub s per y sub s prime at 83 megapascals and 13 hundred killed ones right so using the above equation this y sub s prime is equal to k2 sigma power n exponential times minus q sub c over r t right okay, so this y sub s prime will be 57 .5 per hour times 83 megapascals times power 8 .5 which is the value up in times exponential up...

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