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4 years ago

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A freeway is being designed for a location in rolling terrain. The expected free-flow speed is 55 mi/h. During the peak hour, it

is expected there will be a directional peak-hour volume of 2700 vehicles and 18% heavy vehicles. The PHF is expected to be 0.88. If a level of service no worse than D is desired, determine the necessary number of lanes. (20 points)

1 answer:

balu736 [363]4 years ago

6 0

Answer:

3.

Explanation:

We start calcualting the factor for heavy-vehicle, that is,

$f_{HV} = \frac{1}{1+P_T(E_T-1)+P_R(E_R-1)}$

$E_T = 2.5$ for rolling terrain, so, replacing,

$f_{HV} = \frac{1}{1+0.18(2.5-1)+0}$

$f_{HV} = 0.7874$

We calculate the number of lanes by using the relation as follow:

$N=\frac{V}{\upsilon_p PHF f_{HV} f_p}$

$N=\frac{2700}{1915*0.88*0.7874*1}$

$N= 2.035$

In this way the necessary number of lanes is 3.

Note: To calculate $\upsilon_p$ you need to consult the Exhibit 23-2

in 'Highway capacity Manual' for 55mph and the LOS D criteria.

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A cylindrical specimen of a hypothetical metal alloy is stressed in compression. If its original and final diameters are 30.00 a

kirill [66]

Answer:

105.70 mm

Explanation:

Poisson’s ratio, v is the ratio of lateral strain to axial strain.

E=2G(1+v) where E is Young’s modulus, v is poisson’s ratio and G is shear modulus

Since G is given as 25.4GPa, E is 65.5GPa, we substitute into our equation to obtain poisson’s ratio

$\begin{array}{l}\\65.5{\rm{ GPa}} = 2\left( {25.4{\rm{ GPa}}} \right)(1 + \upsilon )\\\\\upsilon = 0.2893\\\end{array}$

Original length $L_(i}$

$\upsilon = - \left( {\frac{{\left( {\frac{{{d_f} - {d_i}}}{{{d_i}}}} \right)}}{{\left( {\frac{{{L_f} - {L_i}}}{{{L_i}}}} \right)}}} \right)$

Where $d_{f}$ is final diameter, $d_{i}$ is original diameter, $L_{f}$ is final length and $L_{i}$ is original length.

$\begin{array}{l}\\0.2893 = - \left( {\frac{{\left( {\frac{{30.04{\rm{ mm}} - {\rm{30 mm}}}}{{{\rm{30 mm}}}}} \right)}}{{\left( {\frac{{{\rm{105.2 mm}} - {L_i}}}{{{L_i}}}} \right)}}} \right)\\\\\left( {\frac{{{\rm{105.2 mm}} - {L_i}}}{{{L_i}}}} \right) = - 4.6088 \times {10^{ - 3}}\\\end{array}$

$\begin{array}{l}\\105.2 - {L_i} = - \left( {4.6088 \times {{10}^{ - 3}}} \right){L_i}\\\\105.2 = 0.9953{L_i}\\\\{L_i} = 105.70{\rm{ mm}}\\\end{array}$

Therefore, the original length is 105.70 mm

7 0

4 years ago

If a structure can withstand seismic stress, what is it prepared for?.

mars1129 [50]

Answer:

Steel and wood

Explanation:

For a material to resist stress and vibration, it must have high ductility, which is the ability to undergo large deformations and tension. Modern buildings are often constructed with structural steel, a component that comes in a variety of shapes and allows buildings to bend without breaking.

4 0

2 years ago

Given the complex numbers A1 5 6/30 and A2 5 4 1 j5, (a) convert A1 to rectangular form; (b) convert A2 to polar and exponential

Deffense [45]

This question is incomplete, the complete question is;

Given the complex numbers A₁ = 6∠30 and A₂ = 4 + j5;

(a) convert A₁ to rectangular form

(b) convert A₂ to polar and exponential form

(c) calculate A₃ = (A₁ + A₂), giving your answer in polar form

(d) calculate A₄ = A₁A₂, giving your answer in rectangular form

(e) calculate A₅ = A₁/( $A^{*}$ ₂), giving your answer in exponential form.

Answer:

a) A₁ in rectangular form is 5.196 + j3

b) value of A₃ in polar form is 12.19∠41.02°

The polar form of A₂ is 6.403 ∠51.34°, exponential form of A₂ = 6.403 $e^{j51.34 }$

c) value of A₃ in polar form is 12.19∠41.02°

d) A₄ in rectangular form is 5.784 + j37.98

e) A₅ in exponential form is 0.937 $e^{j81.34 }$

Explanation:

Given data in the question;

a) A₁ = 6∠30

we convert A₁ to rectangular form

so

A₁ = 6(cos30° + jsin30°)

= 6cos30° + j6cos30°

= (6 × 0.866) + ( j × 6 × 0.5)

A₁ = 5.196 + j3

Therefore, A₁ in rectangular form is 5.196 + j3

b) A₂ = 4 + j5

we convert to polar and exponential form;

first we convert to polar form

A₂ = √((4)² + (5)²) ∠tan⁻¹( $\frac{5}{4}$ )

= √(16 + 25) ∠tan⁻¹( 1.25 )

= √41 ∠ 51.34°

A₂ = 6.403 ∠51.34°

The polar form of A₂ is 6.403 ∠51.34°

next we convert to exponential form;

A∠β can be written as A $e^{j\beta }$

so, A₂ in exponential form will be;

A₂ = 6.403 $e^{j51.34 }$

exponential form of A₂ = 6.403 $e^{j51.34 }$

c) A₃ = (A₁ + A₂)

giving your answer in polar form

so, A₁ = 6∠30 = 5.196 + j3 and A₂ = 4 + j5

we substitute

A₃ = (5.196 + j3) + ( 4 + j5)

= 9.196 + J8

next we convert to polar

A₃ = √((9.196)² + (8)²) ∠tan⁻¹( $\frac{8 }{9.196}$ )

A₃ = √(84.566416 + 64) ∠tan⁻¹( 0.8699)

A₃ = √148.566416 ∠41.02°

A₃ = 12.19∠41.02°

Therefore, value of A₃ in polar form is 12.19∠41.02°

d) A₄ = A₁A₂

giving your answer in rectangular form

we substitute

A₄ = (5.196 + j3) ( 4 + j5)

= 5.196( 4 + j5) + j3( 4 + j5)

= 20.784 + j25.98 + j12 - 15

A₄ = 5.784 + j37.98

Therefore, A₄ in rectangular form is 5.784 + j37.98

e) A₅ = A₁/( $A^{*}$ ₂)

giving your answer in exponential form

we know that $A^{*}$ ₂ is the complex conjugate of A₂

so

$A^{*}$ ₂ = (6.403 ∠51.34° )*

= 6.403 ∠-51.34°

we convert to exponential form

A∠β can be written as A $e^{j\beta }$

$A^{*}$ ₂ = 6.403 $e^{-j51.34 }$

also

A₁ = 6∠30

we convert to polar form

A₁ = 6 $e^{j30 }$

so A₅ = A₁/( $A^{*}$ ₂)

A₅ = 6 $e^{j30 }$ / 6.403 $e^{-j51.34 }$

A₅ = (6/6.403) $e^{j(30+51.34) }$

A₅ = 0.937 $e^{j81.34 }$

Therefore A₅ in exponential form is 0.937 $e^{j81.34 }$

6 0

3 years ago

melinda is using a rectangular brass bar in a sculpture she is creating. the brass bar has a length that is 4 more than 3 times

lawyer [7]

Answer:

180 x 60 inches

Width = 60 inches

Length = 180 inches

Explanation:

Given

Let L = Length

W = Width

P = Perimeter

Length = 3 * Width

L = 3W

Perimeter of Brass = 480 inches

P = 480

Perimeter is given as 2(L + W);

So, 2 (L + W) = 480

L + W = 480/2

L + W = 240

Substitute 3W for L; so,

3W + W = 240

4W = 240

W = 240/4

W = 60 inches

L = 3W

L = 3 * 60

L = 180 inches

6 0

3 years ago

Read 2 more answers

The purpose of a diamond-shaped yellow sign with black markings is to.

Anit [1.1K]

Answer:

it is to warn you about something like a dead end, or maybe where you should slow down because there might be people crossing ahead.

Explanation:

look at the signs i provided, all of them warn you about something.

Ex: railroad tracks, there might be a train passing, a winding road, so you don't go off road and crash, etc.

4 0

2 years ago