Stress Analysis Problem: Bending and Shear Stress Calculations in SI Units"

In summary, the conversation discusses a homework question about determining the bending stress, shear stress, and torsional stress in a beam with a point load applied at a specific location. The conversation includes a free-body diagram and suggests labeling key points and reaction forces. It also provides guidance on how to approach part (c) of the question, which involves creating functions for the bending moment, transverse shear force, and torsional moment.
  • #1
Precursor
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Homework Statement

(Note: I assumed SI units. So lb=N, inches=m)
[PLAIN]http://img535.imageshack.us/img535/4355/10594047.jpg


The attempt at a solution

For part (a) and (b) I have:

[PLAIN]http://img219.imageshack.us/img219/3049/83432480.jpg


However, how do I go about doing part (c)? Do I use the normal bending stress and shear stress formulas?
 
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  • #2
Precursor said:
(Note: I assumed SI units. So lbf = N, inch = m.)
Excellent.

Precursor: Nice free-body diagram (FBD). Note that Nm should instead be N*m.

When you draw a FBD, you show the dimensions, the applied loads, and the reaction forces. Usually you label key points on a FBD with letters. E.g., you might want to name the point at the origin point A, if you wish, and the other two points B and C. Usually you label the reaction forces as unknowns, such as RAz, MAx, MAy, unless you already know a reaction force with certainty and specifically want to show it as numeric (but usually I still show it as an unknown on the FBD). Notice, your reaction force is correct. But your reaction moments, MAx and MAy, are currently drawn backwards.

No, part (c) does not ask for stress. Write functions for the bending moment, transverse shear force, and torsional moment. The functions will have discontinuities at point B. You could create functions with discontinuities, if you wish. Or you could work it as two separate sets of functions for segments AB and BC, if you wish.
 

FAQ: Stress Analysis Problem: Bending and Shear Stress Calculations in SI Units"

What is stress analysis and why is it important?

Stress analysis is the process of calculating and evaluating the internal forces and deformations that occur in a structure when subjected to external loads. It is important because it helps engineers and scientists ensure that a structure can withstand the expected loads and function safely and efficiently.

What is the difference between bending stress and shear stress?

Bending stress is the stress that occurs in a structure when it is subjected to a bending moment, causing it to bend or deform. Shear stress, on the other hand, is the stress that occurs when two parts of a structure slide past each other in opposite directions. Both types of stress are important to consider in structural analysis.

How do you calculate bending stress in SI units?

The formula for calculating bending stress is σ = M*c/I, where σ is the bending stress, M is the bending moment, c is the distance from the neutral axis to the outermost fiber, and I is the moment of inertia of the cross-section. All of these values can be calculated using SI units, such as meters for distance and Newton-meters for moment.

How do you calculate shear stress in SI units?

The formula for calculating shear stress is τ = V*A/I, where τ is the shear stress, V is the shear force, A is the cross-sectional area, and I is the moment of inertia of the cross-section. Again, all of these values can be calculated using SI units.

Can stress analysis be used for all types of structures?

Yes, stress analysis can be applied to all types of structures, including buildings, bridges, machines, and even biological structures. It is an important tool for ensuring the safety and efficiency of various designs and can be adapted to different materials and loading conditions.

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