# The shrinkage factor and length of beam when it is dried. ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.5, Problem 113E

(a)

To determine

## To evaluate: The shrinkage factor and length of beam when it is dried.

Expert Solution

The shrinkage factor is 0.00055_ and the length of a beam when it has dried is 12.018m_.

### Explanation of Solution

Given:

If a concrete beam has a water content of wkg/m3, then it will shrink by a factor S=0.032w2.510,000, where S is the fraction of the original beam length that disappears due to shrinkage.

That is, S=LengththatdisappearsduetoshrinkageOriginallengthofbeam.

Calculation:

Given that the water content in the concrete is 250kg/m3.

Substitute 250 for w in the equation S=0.032w2.510,000.

S=0.032×2502.510,000=82.510,000=5.510,000=0.00055

Thus, the shrinkage factor in concrete beam is 0.00055_.

Note that, the length of the beam is 12.025 m.

Substitute 0.00055 for S and 12.025 for original length of beam in the equation S=LengththatdisappearsduetoshrinkageOriginallengthofbeam.

0.00055=Lengththatdisappearsduetoshrinkage12.025Lengththatdisappearsduetoshrinkage=0.00055×12.025Lengththatdisappearsduetoshrinkage=0.0066

Therefore, the length that disappears due to shrinkage is 0.0066m.

Length of beam when it has dried=[Original length of beamLength that disappears due to shrinkage]

Substitute 12.025 for original length of beam and 0.0066 for length that disappears due to shrinkage.

Length of beam when it has dried=12.0250.0066Length of beam when it has dried=12.018

Length of beam when it has dried is 12.018m.

Thus, length of beam when it has dried is 12.018m_.

(b)

To determine

### The water content in concrete beam.

Expert Solution

The water content in concrete beam is 234.375kg/m3_.

### Explanation of Solution

The shrinkage factor is obtained as 0.00050.

Substitute 0.00050 for S in the equation S=0.032w2.510,000.

0.00050=0.032×w2.510,0000.00050×10,000=0.032w2.50.032w2.5=5

Simplify the above equation as follows.

0.032w=5+2.50.032w=7.5w=7.50.032w=234.375

Thus, the water content in concrete beam is 234.375kg/m3_.

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