# Total Load per Unit Length

on . Posted in Structural Engineering

Total load per unit length, abbreviated as $$w'$$, is the amount of force or weight applied to a structure or object over a specific length.  Compressive stress is the force that is responsible for the deformation of the material such that the volume of the material reduces.  It is commonly used in engineering and physics to determine the stress or strain on a component or structural element.

This concept is commonly used in engineering and physics to analyze the stresses and strains in various structures and materials, such as beams, cables, or rods, to ensure they can withstand the applied loads without failure.  Understanding the total load per unit length is crucial for designing safe and efficient structures.

### Total load per unit length formula

$$w' \;=\; ( t \; \sigma_c ) - w$$     (Total Load per Unit Length)

$$t \;=\; w' + w \;/\ \sigma_c$$

$$\sigma_c \;=\; w' + w \;/\ 2 \; t$$

$$w \;=\; ( t \; \sigma_c ) - w'$$

### Solve for w'

 thickness, t compressive stress, σc load per unit length, w

### Solve for t

 total load per unit length, w' load per unit length, w compressive stress, σc

### Solve for σc

 total load per unit length, w' load per unit length, w thickness, t

### Solve for w

 thickness, t compressive stress, σc total load per unit length, w'

Symbol English Metric
$$w'$$ = total load per unit length $$lbf\;/\;in$$  $$N\;/\;m$$
$$t$$ = thickness through an object $$in$$  $$m$$
$$\sigma_c$$ (Greek symbol sigma) = compressive stress $$lbf\;/\;in^2$$  $$Pa$$
$$w$$ = load per unit length $$lbf\;/\;in$$  $$N\;/\;m$$

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