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Nady [450]
3 years ago
11

Could I please get help with this​

Engineering
1 answer:
alex41 [277]3 years ago
5 0

Answer:

1.I_{xc} = 7.161458\overline 3 in.⁴

I_{yc} = 36.661458\overline 3 in.⁴

Iₓ = 28.6458\overline 3 in.⁴

I_y = 138.6548\overline 3 in.⁴

2. I_{xc} = 114.\overline 3 in.⁴

I_{yc} = 37.\overline 3 in.⁴

Iₓ = 457.\overline 3 in.⁴

I_y = 149.\overline 3 in.⁴

3. The maximum deflection of the beam is 2.55552 inches

Explanation:

1. The height of the beam having a rectangular cross section is h = 2.5 in.

The breadth of the beam, is = 5.5 in.

The moment of inertia of a rectangular beam through its centroid is given as follows;

I_{xc} = b·h³/12 = 5.5 × 2.5³/12 = 1375/192 = 7.161458\overline 3

I_{xc} = 7.161458\overline 3 in.⁴

I_{yc} = h·b³/12 = 2.5 × 5.5³/12 = 6655/192 = 36.661458\overline 3

I_{yc} = 36.661458\overline 3 in.⁴

The moment of inertia about the base is given as follows;

Iₓ = b·h³/3 = 5.5 × 2.5³/3 = 625/24 = 28.6458\overline 3

Iₓ = 28.6458\overline 3 in.⁴

I_y = h·b³/3 = 2.5 × 5.5³/3 = 6655/48= 138.6548\overline 3

I_y = 138.6548\overline 3 in.⁴

2. The height of the beam having a rectangular cross section is h = 7 in.

The breadth of the beam, b = 4 in.

The moment of inertia of a rectangular beam through its centroid is given as follows;

I_{xc} = b·h³/12 = 4 × 7³/12 = 114.\overline 3

I_{xc} = 114.\overline 3 in.⁴

I_{yc} = h·b³/12 = 7 × 4³/12 = 37.\overline 3

I_{yc} = 37.\overline 3 in.⁴

The moment of inertia about the base is given as follows;

Iₓ = b·h³/3 = 4 × 7³/3 = 457.\overline 3

Iₓ = 457.\overline 3 in.⁴

I_y = h·b³/3 = 2.5 × 5.5³/3 = 149.\overline 3

I_y = 149.\overline 3 in.⁴

3. The deflection, \delta _{max}, of a simply supported beam having a point load at the center is given as follows;

\delta_{max} = \dfrac{W \times L^3}{48 \times E \times I}

The given parameters of the beam are;

The length of the beam, L = 22 ft. = 264 in.

The applied load at the center, W = 750 lbs

The modulus of elasticity for Cedar = 10,000,000 psi

The height of the wood, h = 3 in.

The breadth of the wood, b = 5 in.

The moment of inertia of the wood, I_{xc} = b·h³/12 = 5 × 3³/12 = 11.25 in.⁴

By plugging in the given values, we have;

\delta_{max} = \dfrac{750 \times 264^3}{48 \times 10,000,000 \times 11.25} = 2.55552

The maximum deflection of the beam, \delta _{max} = 2.55552 inches

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Answer:

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Explanation:

To calculate the heat required for the given process Q, we recall the energy balance equation.

Therefore, : Q = Δ U = m (u₂ - u₁) ..................equation (1)

We should note that there are no kinetic or potential energy change so the heat input in the system is converted only to internal energy.

Therefore, we will start the equation with the mass of the water (m) using given the initial percentage quality as x₁ = 0.123 and initial temperature t₁ = 100⁰c , we can them determine the initial specific volume v₁ of the mixture. For the calculation, we will also need the specific volume of liquid vₙ  = 0.001043m³/kg and water vapour (vₐ) = 1.6720m³/kg

Therefore, u₁ = vₙ + x₁ . ( vₐ - vₙ)

                   u₁ = 0.001043m³/kg + 0.123 . ( 1.6720m³/kg - 0.001043m³/kg)

                   u₁ = 0.2066m³/kg

Moving forward, the mass of the vapor can then be calculated using the given volume of tank V = 14 L but before the calculation, we need to convert the volume to from liters to m³.

Therefore, V = 14L . 1m² / 1000L = 0.014 m³

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Therefore, u₁ = vₐ + x₁ . vₐₙ

                   u₁ = 419.06 kj / kg + 0.123  .  2087.0 kj/kg

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For the final specific internal energy u₂, we first need to calculate the final quality of the mixture x₂ . The tank is rigid meaning the volume does not change and it is also closed meaning the mass does not change.from this, we can conclude the the specific volume also does not change during the process u₁ = u₂. This allows us to use the given final temperature T₂ = 180⁰c to determine the final quality x₂ of the mixture. for the calculation, we will also need the specific volume of liquid vₙ=0.001091m³/kg and vapor vₐ =  0.39248m³/kg

Hence, x₂ = u₂ - vₙ / uₐ

x₂ = 0.2066 m³/kg - 0.001091m³/kg / 0.39248m³/kg

x₂ = 0.524

Moving forward to calculate the final internal energy u₂, we have :

u₂ = vₙ + x₂ . vₙₐ

u₂ = 631.66 kj/kg + 0.524  . 1927.4 kj/kg

u₂ = 1641.62 kj/kg

We now return to equation (1) to plug in the values generated thus far

Q = m (u₂ - u₁)

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Q = 65.388KJ

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