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mash [69]
2 years ago
12

Show that p must be directed through centroids of cross sections if axial stress ? is not to vary over a cross section.

Mathematics
1 answer:
wolverine [178]2 years ago
7 0
Assuming P (usually written in upper case) represents a force normal to a given cross section.

If a point load is applied to any point of the section, stress concentration will cause axial stress to vary.

The context of the question considers the uniformity of axial stress at a certain distance away from the point of application (thus stress concentration can be neglected).

If a force P is applied through the centroid, sections will be stressed uniformly.  However, if the force P is applied at a distance "e" from the centroid, the equivalent load on the section equals an axial force and a moment Pe.  The latter causes bending of the member, causing non-uniform stress.

If we assume A=(uniform) cross sectional area, and I=moment of inertia of the section, then stress varies with the distance y from the centroid equal to
stress=sigma=P/A + My/I
where P=axial force, M=moment = Pe.
Therefore when e>0, the stress varies across the section.
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Find the value of $B - A$ if the graph of $Ax + By = 3$ passes through the point $(-7,2),$ and is parallel to the graph of $x +
Salsk061 [2.6K]

Answer:

-6

Step-by-step explanation:

We know that since Ax + By = 3 passes through (-7, 2), then if we plug -7 in for x and 2 in for y, the equation is satisfied. So, let's do that:

Ax + By = 3

A * (-7) + B * 2 = 3

-7A + 2B = 3

We also know that this line is parallel to x + 3y = -5, which means their slopes are the same. Let's solve for y in the second equation:

x + 3y = -5

3y = -x - 5

y = (-1/3)x - (5/3)

So, the slope of this line is -1/3, which means the slope of Ax + By = 3 is also -1/3. Let's solve for y in the first equation:

Ax + By = 3

By = -Ax + 3

y = (-A/B)x + 3/B

This means that -A/B = -1/3. So, we have a relationship between A and B:

-A/B = -1/3

A/B = 1/3

B = 3A

Plug 3A in for B into the equation we had where -7A + 2B = 3:

-7A + 2B = 3

-7A + 2 * 3A = 3

-7A + 6A = 3

-A = 3

A = -3

Use this to solve for B:

B = 3A

B = 3 * (-3) = -9

So, B = -9 and A = -3. Then B - A is:

B - A = -9 - (-3) = -9 + 3 = -6

The answer is -6.

<em>~ an aesthetics lover</em>

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f the pattern in the table is extended to represent more equivalent ratios for 2:6, which pair of numbers would be in the column
olasank [31]

The pair of numbers that would be in the columns, considering the proportional relationship, is given as follows:

20 would be in the column for 2, and 60 would be in the column for 6.

<h3>What is a proportional relationship?</h3>

A proportional relationship is a special linear function, with intercept having a value of zero, in which the output variable is obtained with the multiplication of the input variable and the constant of proportionality k, as shown as follows:

y = kx

The table is extended to represent more equivalent ratios for 2:6, hence the constant of the relationship is given as follows:

k = 6/2 = 3.

Hence the equation is:

y = 3x.

The values given by each column are given as follows:

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When x = 20, the numeric value of the relationship is of:

y = 3 x 20 = 60.

Hence the first option is correct.

More can be learned about proportional relationships at brainly.com/question/10424180

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