Engr Help

Symbolic Solutions

Key Concept: Values of forces (F), moments (M), dimensions such as lengths (L) and

angles (θ) as well as variables such as stress (σ), strain (ε), shear stress (τ) and material

properties such as Young's Modulus (E), Shearing Modulus (G) and Poisson's ratio (ν)

are typically provided as input information in assigned problems. You are then asked to find

some result such as normal, bending, or shear stress.

A preferred approach is to use symbols rather than their values as you step through your solution

and is highly recommended. This approach has two distinct benefits.

Benefits of using Symbolic Solutions

Benefit 1

As you proceed through your solution you can check the

dimensions of each term to verify that at each stage of the

solution your results check dimensionally. If they do, then

your calculations are possibly correct. If not, then you have

an error somewhere and you should review the steps leading

up to your result.

i.e. σ = P / A where σ is the normal stress

P is the load and A is the area

Check dimensions:

equation: σ = P / A

dimensions: F/L² = F / L² (check)

Benefit 2

When you arrive at your final result you can investigate the

influence of each variable or parameter on the unknown

being calculated.

Also for on-line, assigned problems, the values of input variables

may change. So your symbolic solution will be valid for any set

of input data. You can simply enter the latest set of input data to arrive at your answer.

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