A geotechnical problem uses Effective stress. Given total stress (sigma) = 4,820 psf; pore pressure (u) = 2,800 psf, determine the effective stress (sigmap) in psf.

Start with the thinking

• The governing relation printed in this handbook section is Effective stress.
• Everything except sigmap is given, so isolate sigmap symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Geotechnical items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\sigma' = \sigma - u$$

2. Step 2 — Rearrange the relation so that sigmap stands alone on the left-hand side.

3. Step 3

   $$List the givens: total stress (sigma) = 4,820 psf, pore pressure (u) = 2,800 psf$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$sigmap = 2020\ \text{psf}$$

6. Step 6 — Check: returning sigmap = 2,020 psf to

   $$\sigma' = \sigma - u$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 4,040 — kept a factor of two that cancels in the correct rearrangement.
• 1,010 — dropped that same factor in the other direction.
• 2,222 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Geotechnical → Effective stress

A geotechnical problem uses Effective stress. Given pore pressure (u) = 1,710 psf; effective stress (sigmap) = 1,057 psf, determine the total stress (sigma) in psf.

Start with the thinking

• The governing relation printed in this handbook section is Effective stress.
• Everything except sigma is given, so isolate sigma symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Geotechnical items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\sigma' = \sigma - u$$

2. Step 2 — Rearrange the relation so that sigma stands alone on the left-hand side.

3. Step 3

   $$List the givens: pore pressure (u) = 1,710 psf, effective stress (sigmap) = 1,057 psf$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$\sigma = 2767\ \text{psf}$$

6. Step 6 — Check: returning sigma = 2,767 psf to

   $$\sigma' = \sigma - u$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 5,534 — kept a factor of two that cancels in the correct rearrangement.
• 1,384 — dropped that same factor in the other direction.
• 3,044 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Geotechnical → Effective stress

A geotechnical problem uses Effective stress. Given total stress (sigma) = 5,700 psf; effective stress (sigmap) = 7,801 psf, determine the pore pressure (u) in psf.

Start with the thinking

• The governing relation printed in this handbook section is Effective stress.
• Everything except u is given, so isolate u symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Geotechnical items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\sigma' = \sigma - u$$

2. Step 2 — Rearrange the relation so that u stands alone on the left-hand side.

3. Step 3

   $$List the givens: total stress (sigma) = 5,700 psf, effective stress (sigmap) = 7,801 psf$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$u = -2101\ \text{psf}$$

6. Step 6 — Check: returning u = -2,101 psf to

   $$\sigma' = \sigma - u$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• -4,202 — kept a factor of two that cancels in the correct rearrangement.
• -1,051 — dropped that same factor in the other direction.
• -2,311 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Geotechnical → Effective stress

A geotechnical problem uses Effective stress. Given total stress (sigma) = 2,570 psf; pore pressure (u) = 2,890 psf, determine the effective stress (sigmap) in psf.

Start with the thinking

• The governing relation printed in this handbook section is Effective stress.
• Everything except sigmap is given, so isolate sigmap symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Geotechnical items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\sigma' = \sigma - u$$

2. Step 2 — Rearrange the relation so that sigmap stands alone on the left-hand side.

3. Step 3

   $$List the givens: total stress (sigma) = 2,570 psf, pore pressure (u) = 2,890 psf$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$sigmap = -320.0\ \text{psf}$$

6. Step 6 — Check: returning sigmap = -320.0 psf to

   $$\sigma' = \sigma - u$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• -640.0 — kept a factor of two that cancels in the correct rearrangement.
• -160.0 — dropped that same factor in the other direction.
• -352.0 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Geotechnical → Effective stress

A geotechnical problem uses Effective stress. Given pore pressure (u) = 2,330 psf; effective stress (sigmap) = 1,307 psf, determine the total stress (sigma) in psf.

Start with the thinking

• The governing relation printed in this handbook section is Effective stress.
• Everything except sigma is given, so isolate sigma symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Geotechnical items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\sigma' = \sigma - u$$

2. Step 2 — Rearrange the relation so that sigma stands alone on the left-hand side.

3. Step 3

   $$List the givens: pore pressure (u) = 2,330 psf, effective stress (sigmap) = 1,307 psf$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$\sigma = 3637\ \text{psf}$$

6. Step 6 — Check: returning sigma = 3,637 psf to

   $$\sigma' = \sigma - u$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 7,274 — kept a factor of two that cancels in the correct rearrangement.
• 1,819 — dropped that same factor in the other direction.
• 4,001 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Geotechnical → Effective stress

A geotechnical problem uses Effective stress. Given total stress (sigma) = 6,170 psf; effective stress (sigmap) = 2,397 psf, determine the pore pressure (u) in psf.

Start with the thinking

• The governing relation printed in this handbook section is Effective stress.
• Everything except u is given, so isolate u symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Geotechnical items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\sigma' = \sigma - u$$

2. Step 2 — Rearrange the relation so that u stands alone on the left-hand side.

3. Step 3

   $$List the givens: total stress (sigma) = 6,170 psf, effective stress (sigmap) = 2,397 psf$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$u = 3773\ \text{psf}$$

6. Step 6 — Check: returning u = 3,773 psf to

   $$\sigma' = \sigma - u$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 7,546 — kept a factor of two that cancels in the correct rearrangement.
• 1,887 — dropped that same factor in the other direction.
• 4,150 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Geotechnical → Effective stress

A geotechnical problem uses Effective stress. Given total stress (sigma) = 6,290 psf; pore pressure (u) = 3,080 psf, determine the effective stress (sigmap) in psf.

Start with the thinking

• The governing relation printed in this handbook section is Effective stress.
• Everything except sigmap is given, so isolate sigmap symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Geotechnical items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\sigma' = \sigma - u$$

2. Step 2 — Rearrange the relation so that sigmap stands alone on the left-hand side.

3. Step 3

   $$List the givens: total stress (sigma) = 6,290 psf, pore pressure (u) = 3,080 psf$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$sigmap = 3210\ \text{psf}$$

6. Step 6 — Check: returning sigmap = 3,210 psf to

   $$\sigma' = \sigma - u$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 6,420 — kept a factor of two that cancels in the correct rearrangement.
• 1,605 — dropped that same factor in the other direction.
• 3,531 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Geotechnical → Effective stress

A geotechnical problem uses Effective stress. Given pore pressure (u) = 1,550 psf; effective stress (sigmap) = 6,514 psf, determine the total stress (sigma) in psf.

Start with the thinking

• The governing relation printed in this handbook section is Effective stress.
• Everything except sigma is given, so isolate sigma symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Geotechnical items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\sigma' = \sigma - u$$

2. Step 2 — Rearrange the relation so that sigma stands alone on the left-hand side.

3. Step 3

   $$List the givens: pore pressure (u) = 1,550 psf, effective stress (sigmap) = 6,514 psf$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$\sigma = 8064\ \text{psf}$$

6. Step 6 — Check: returning sigma = 8,064 psf to

   $$\sigma' = \sigma - u$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 16,128 — kept a factor of two that cancels in the correct rearrangement.
• 4,032 — dropped that same factor in the other direction.
• 8,870 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Geotechnical → Effective stress

A geotechnical problem uses Effective stress. Given total stress (sigma) = 1,680 psf; effective stress (sigmap) = 7,257 psf, determine the pore pressure (u) in psf.

Start with the thinking

• The governing relation printed in this handbook section is Effective stress.
• Everything except u is given, so isolate u symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Geotechnical items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\sigma' = \sigma - u$$

2. Step 2 — Rearrange the relation so that u stands alone on the left-hand side.

3. Step 3

   $$List the givens: total stress (sigma) = 1,680 psf, effective stress (sigmap) = 7,257 psf$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$u = -5577\ \text{psf}$$

6. Step 6 — Check: returning u = -5,577 psf to

   $$\sigma' = \sigma - u$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• -11,154 — kept a factor of two that cancels in the correct rearrangement.
• -2,789 — dropped that same factor in the other direction.
• -6,135 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Geotechnical → Effective stress

A geotechnical problem uses Effective stress. Given total stress (sigma) = 3,080 psf; pore pressure (u) = 3,850 psf, determine the effective stress (sigmap) in psf.

Start with the thinking

• The governing relation printed in this handbook section is Effective stress.
• Everything except sigmap is given, so isolate sigmap symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Geotechnical items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\sigma' = \sigma - u$$

2. Step 2 — Rearrange the relation so that sigmap stands alone on the left-hand side.

3. Step 3

   $$List the givens: total stress (sigma) = 3,080 psf, pore pressure (u) = 3,850 psf$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$sigmap = -770.0\ \text{psf}$$

6. Step 6 — Check: returning sigmap = -770.0 psf to

   $$\sigma' = \sigma - u$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• -1,540 — kept a factor of two that cancels in the correct rearrangement.
• -385.0 — dropped that same factor in the other direction.
• -847.0 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Geotechnical → Effective stress