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Papessa [141]
3 years ago
7

The beam is supported by a pin at A and a roller at B which has negligible weight and a radius of 15 mm. If the coefficient of s

tatic friction is mB = mC = 0.3, determine the largest angle u of the incline so that the roller does not slip for any force P applied to the beam.
Engineering
1 answer:
Anettt [7]3 years ago
5 0

Answer:

33.4

Explanation:

Step 1:

\sumMo=0 (moment about the origin)

Fb(15)-Fc(15)=0

Fb=Fc

Step 2:

\sumFx=0

-Fb-Fccos\theta+Ncsin\theta=0

Fc=0.3Nc=Fb

-0.3Nc-0.3Nccos\theta+Ncsin\theta=0

(-0.3-cos\theta+sin\theta)Nc=0----(1)

\sumFy=0

Nccos\theta+Fcsin\theta-Nb=0

Nccos\theta+0.3Ncsin\theta-Nc=0

Nc[cos\theta+0.3sin\theta-1]=0--------(2)

Solving eq (1) and eq (2)

\theta=33.4

Step 3:

As the roller is a two force member

2(90-\phi)+\theta=180

\phi=\theta/2

\phi=Tan(\muN/N)-1

\phi=16.7

\theta=2x16.7=33.4

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A compressible clay layer has a thickness of 3.8 m. After 1.5 yr, when the clay is 50% consolidated, 7.3 cm of settlement has oc
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The amount of settlement that would occur at the end of 1.5 year and 5 year are 7.3 cm and 13.14 cm respectively.

<h3>How to determine the amount of settlement?</h3>

For a layer of 3.8 m thickness, we were given the following parameters:

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At 50%, the time for a layer of 38 m thickness is:

t_{50} = 1.5 × (38/3.8)²

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For the thickness of 38 m, U₂ is given by:

\frac{U_1^2}{U_2^2} =\frac{(T_v)_1}{(T_v)_2} = \frac{t_1}{t_2} \\\\U_2^2 = U_1^2 \times [\frac{t_2}{t_1} ]\\\\U_2^2 = 0.5^2 \times [\frac{1.5}{150} ]\\\\U_2^2 = 0.25  \times 0.01\\\\U_2=\sqrt{0.0025} \\\\U_2=0.05

The new settlement after 1.5 year is:

Sc = U₂Sf

Sc = 0.05 × 146

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For time, t₂ = 5 year:

U_2^2 = U_1^2 \times [\frac{t_2}{t_1} ]\\\\U_2^2 = 0.5^2 \times [\frac{5}{150} ]\\\\U_2^2 = 0.25  \times 0.03\\\\U_2=\sqrt{0.0075} \\\\U_2=0.09

The new settlement after 5 year is:

Sc = U₂Sf

Sc = 0.09 × 146

Sc = 13.14 cm.

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8 0
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Answer:

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The thrust generated is 15300 N.

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