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3 years ago

What is the significance of Saint Venant's principle?

Engineering

1 answer:

nexus9112 [7]3 years ago

7 0

Answer:

While calculating the stresses in a body since we we assume a constant distribution of stress across a cross section if the body is loaded along the centroid of the cross section , this assumption of uniformity is assumed only on the basis of Saint Venant's Principle.

Saint venant principle states that the non uniformity in the stress at the point of application of load is only significant at small distances below the load and depths greater than the width of the loaded material this non uniformity is negligible and hence a uniform stress distribution is a reasonable and correct assumption while solving the body for stresses thus greatly simplifying the analysis.

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With a very precise volumetric measuring device, the volume of a liquid sample is determined to be 6.321 L (liters). Three stude

zheka24 [161]

Answer:

See explanation

Explanation:

Solution:-

- Three students measure the volume of a liquid sample which is 6.321 L.

- Each student measured the liquid sample 4 times. The data is provided for each measurement taken by each student as follows:

Students

Trial A B C

1 6.35 6.31 6.38

2 6.32 6.31 6.32

3 6.33 6.32 6.36

4 6.36 6.35 6.36

- We will define the two terms stated in the question " precision " and "accuracy"

- Precision refers to how close the values are to the sample mean. The dense cluster of data is termed to be more precise. We will use the knowledge of statistics and determine the sample standard deviation for each student.

- The mean measurement taken by each student would be as follows:

$E ( A ) = \frac{6.35 +6.32+6.33+6.36}{4} \\\\E ( A ) = 6.34\\\\E ( B ) = \frac{6.31 +6.31+6.32+6.35}{4} \\\\E ( B ) = 6.3225\\\\E ( C ) = \frac{6.38 +6.32+6.36+6.36}{4} \\\\E ( C ) = 6.355\\$

- The precision can be quantize in terms of variance or standard deviation of data. Therefore, we will calculate the variance of each data:

$Var ( A ) = \frac{6.35^2+6.32^2+6.33^2+6.36^2}{4} - 6.34^2\\\\Var ( A ) = 0.00025\\\\Var ( B ) = \frac{6.31^2+6.31^2+6.32^2+6.35^2}{4} - 6.3225^2\\\\Var ( B ) = 0.00026875\\\\Var ( C ) = \frac{6.38^2+6.32^2+6.36^2+6.36^2}{4} - 6.355^2\\\\Var ( C ) = 0.000475\\$

- We will rank each student sample data in term sof precision by using the values of variance. The smallest spread or variance corresponds to highest precision. So we have:

Var ( A ) < Var ( B ) < Var ( C )

most precise Least precise

- Accuracy refers to how close the sample mean is to the actual data value. Where the actual volume of the liquid specimen was given to be 6.321 L. We will evaluate the percentage difference of sample values obtained by each student .

$P ( A ) = \frac{6.34-6.321}{6.321}*100= 0.30058\\\\P ( B ) = \frac{6.3225-6.321}{6.321}*100= 0.02373\\\\P ( C ) = \frac{6.355-6.321}{6.321}*100= 0.53788\\$

- Now we will rank the sample means values obtained by each student relative to the actual value of the volume of liquid specimen with the help of percentage difference calculated above. The least percentage difference corresponds to the highest accuracy as follows:

P ( B ) < P ( A ) < P ( C )

most accurate least accurate

7 0

3 years ago

A 10-mm-diameter Brinell hardness indenter produced an indentation 1.55 mm in diameter in a steel alloy when a load of 500 kg wa

BigorU [14]

Answer:

HB = 3.22

Explanation:

The formula to calculate the Brinell Hardness is given as follows:

$HB = \frac{2P}{\pi D\sqrt{D^{2}- d^{2} } }$

where,

HB = Brinell Hardness = ?

P = Applied Load in kg = 500 kg

D = Diameter of Indenter in mm = 10 mm

d = Diameter of the indentation in mm = 1.55 mm

Therefore, using these values, we get:

$HB = \frac{(2)(500)}{\pi (10)\sqrt{10^{2}- 1.55^{2} } }$

4 0

3 years ago

9. An embankment having a volume of 320,000 yd is to be constructed from local borrow. The dry unit weight and moisture content

tatuchka [14]

Answer:

correct option is (B) 315,500

Explanation:

given data

volume = 320,000 yd³ = 8640000 ft³

dry unit weight = 106 pcf

moisture content = 18.2%

total unit weight = 122 pcf

moisture content = 16.7%

to find out

volume of borrow lyd needed

solution

first we get here weight of material that is

weight = volume × unit weight

weight = 8640000 × 122

weight = 1054080000 lb

that weight is weight of water + weight of solid so

0.167 × weight is weight of water + weight of solid ) = 1054080000 lb

and weight of solid = $\frac{1054080000}{1.167}$

weight of soil solid is = 903239075 pound

and weight of water = 150840925 pound

so volume of soil = 903239075 ÷ 106 lb/ft³ = 8521123.34 ft³

and volume required = 8521123.34 ft³ ÷ 27 ft³ = 315597.161 yd³

volume required = 315500 yd³

so correct option is (B) 315,500

3 0

3 years ago

The accompanying specific gravity values describe various wood types used in construction. 0.320.350.360.360.370.380.400.400.40

marysya [2.9K]

Answer:

$\begin{array}{ccc}{Steam} & {\vert} & {Leaf} \ \\ \\ {0.3} & {\vert} & {2\ 5\ 6\ 6\ 7\ 8} \ \\ \\{0.4} & {\vert} & {0\ 0\ 0\ 1\ 1\ 2\ 2\ 2\ 2\ 2\ 3\ 4\ 5\ 6\ 6\ 7\ 8\ 8\ 9} \ \\ \ \\ {0.5} & {\vert} & {1\ 4\ 4\ 5\ 8} \ \\ \ \\ {0.6} & {\vert} & {3\ 6\ 6\ 7\ 8} \ \\ \ \\ {0.7} & {\vert} & {8} \ \ \end{array}$