In order for an aircraft to spin, it must be placed in a specific flight condition known as an aggravated stall. This occurs when the angle of attack of the aircraft is too high and the airflow over the wings becomes disrupted, causing a loss of lift.
As a result, one wing may stall before the other, creating an unequal lift distribution that can cause the aircraft to enter a spin. Pilots must be trained to recognize and recover from this dangerous situation in order to prevent accidents.
In order to spin, an aircraft must be placed in a specific flight condition known as a "stall." A stall occurs when the angle of attack is too high, causing a reduction in lift and an increase in drag. To initiate a spin, the aircraft must be in a stalled condition and have a yawing motion (rotation around the vertical axis). This combination of factors causes one wing to generate more lift than the other, resulting in the spinning motion.
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In order for an aircraft to spin, it must be in a stall condition. A stall occurs when the angle of attack (AOA) is too high, causing the airflow over the wings to separate and the lift generated by the wings to decrease. When the AOA reaches the critical angle of attack, the airflow can no longer create enough lift to keep the aircraft in the air, and it begins to descend.
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A rectangular brick-lined channel (n = 0.016) of 4.0-m width is laid on a bottom slope of 0.0009. It carries a discharge of 15 m3 /s and the fl ow is non-uniform. If the depth at a Section A is 2.6 m, calculate the depth at section B, 500 m downstream of A, by using (a) only one step, and (b) two steps.
Answer:
To calculate the depth at section B, 500 m downstream of section A, we can use the Chezy formula:
V = C*R^(1/2)
Where V is the velocity, C is the Chezy coefficient, and R is the hydraulic radius.
a) Using only one step:
Since the flow is non-uniform, the velocity at section B can be assumed to be the same as at section A. Therefore, the depth at section B can be calculated using the same Chezy coefficient and hydraulic radius as at section A.
Hydraulic Radius (R) = A/P = (width * depth) / 2
R_A = (4 * 2.6) / 2 = 5.2 m
R_B = R_A = 5.2 m
Chezy coefficient (C) = (V^2 * n) / (2 * g * R^(1/2))
C = (15^2 * 0.016) / (2 * 9.81 * 5.2^(1/2)) = 1.94
Now we can use the Chezy formula to calculate the depth at section B
V = C*R^(1/2)
V = 1.94 * 5.2^(1/2) = 3.23 m/s
b) Using two steps:
First, we can calculate the velocity at section B using the continuity equation:
Q = A1 * V1 = A2 * V2
15 = (4 * 2.6 * 3.23) = (4 * y * V2)
V2 = (15 / 4) / y = 3.75/y m/s
Next, we can use the Chezy formula and the velocity at section B to calculate the depth at section B:
V = C*R^(1/2)
y = V^2 * n / (C^2 * g)
y = (3.75/y)^2 * 0.016 / (1.94^2 * 9.81)
y = 2.34 m
So, the depth at section B is 2.34 m by using two steps.
Note: The above calculations are based on the assumption that the slope is uniform along the channel and the flow is steady. In practice, other factors such as channel roughness and boundary conditions may also have an impact on the depth of flow.
fraternity house with 40 occupants is considered a Group pancy. a. R-1 c. R-3 Reference b. R-2 d.
A fraternity house with 40 occupants is considered a Group A fraternity house with 40 occupants is considered a Group R-2 occupancy. The correct option is B.
What is a fraternity house?Fraternity and sorority housing in North America primarily refers to the residences or communities where members of these organizations live and socialize. Fraternity and sorority housing can serve as a place to live as well as a place to host social events, meetings, and community-oriented activities.
When there are 40 residents living in a fraternity house, it is referred to as a Group R-2 occupancy. Therefore, based on the information, the correct option is B.
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Assignment 1: Structural Design of Rectangular Reinforced Concrete Beams for Bending
Perform structural design of a rectangular reinforced concrete beam for bending. The beam is simply supported and has a span L=20 feet. In addition to its own weight the beam should support a superimposed dead load of 0.50 k/ft and a live load of 0.65 k/ft. Use a beam width of 12 inches. The depth of the beam should satisfy the ACI stipulations for minimum depth and be proportioned for economy. Concrete compressive strength f’c = 4,000 psi and yield stress of reinforcing bars fy = 60,000 psi. Size of stirrups should be chosen based on the size of the reinforcing bars. The beam is neither exposed to weather nor in contact with the ground, meaning it is subjected to interior exposure.
• Use the reference on "Practical Considerations for Rectangular Reinforced Concrete Beams"
• Include references to ACI code – see slides from second class
• Include references to Tables from Appendix A
• Draw a sketch of the reinforced concrete beam showing all dimensions, number and size of rebars, including stirrups.
Answer:
Beam of 25" depth and 12" width is sufficient.
I've attached a detailed section of the beam.
Explanation:
We are given;
Beam Span; L = 20 ft
Dead load; DL = 0.50 k/ft
Live load; LL = 0.65 k/ft.
Beam width; b = 12 inches
From ACI code, ultimate load is given as;
W_u = 1.2DL + 1.6LL
Thus;
W_u = 1.2(0.5) + 1.6(0.65)
W_u = 1.64 k/ft
Now, ultimate moment is given by the formula;
M_u = (W_u × L²)/8
M_u = (1.64 × 20²)/8
M_u = 82 k-ft
Since span is 20 ft, it's a bit larger than the average span beams, thus, let's try a depth of d = 25 inches.
Effective depth of a beam is given by the formula;
d_eff = d - clear cover - stirrup diameter - ½Main bar diameter
Now, let's adopt the following;
Clear cover = 1.5"
Stirrup diameter = 0.5"
Main bar diameter = 1"
Thus;
d_eff = 25" - 1.5" - 0.5" - ½(1")
d_eff = 22.5"
Now, let's find steel ratio(ρ) ;
ρ = Total A_s/(b × d_eff)
Now, A_s = ½ × area of main diameter bar
Thus, A_s = ½ × π × 1² = 0.785 in²
Let's use Nominal number of 3 bars as our main diameter bars.
Thus, total A_s = 3 × 0.785
Total A_s = 2.355 in²
Hence;
ρ = 2.355/(22.5 × 12)
ρ = 0.008722
Design moment Capacity is given;
M_n = Φ * ρ * Fy * b * d²[1 – (0.59ρfy/fc’)]/12
Φ is 0.9
f’c = 4,000 psi = 4 kpsi
fy = 60,000 psi = 60 kpsi
M_n = 0.9 × 0.008722 × 60 × 12 × 22.5²[1 - (0.59 × 0.008722 × 60/4)]/12
M_n = 220.03 k-ft
Thus: M_n > M_u
Thus, the beam of 25" depth and 12" width is sufficient.
Standards relating to technical drawing
Answer:
Borders, Dimensions Identified, Scale, Text Box with Date/Author/Title/Version Number
Explanation:
Technical drawings have many standards in order to maintain integrity and ensure that they can be used by engineers to produce what is mapped out in the drawing.
Every technical drawing needs to have borders and a text box with all information related to the drawing. This includes the date it was created, date it was updated, version number, title, and author.
Furthermore, each drawing should have necessary dimensions with a scale. At the same time, technical drawings should not be over-dimensioned or repetitive.
All of these things must be on a technical drawing to allow professional engineers to sign off on drawings.
Discuss the capabilities that should be provided by a DBMS.
Answer:
They include;
1. A database backup and recovery system.
2. A good security architecture
3. Concurrent access to the system
4. Data dictionary
5. Data definition
6. Data Manipulation Language
Explanation:
A Database Management system shortened as DBMS is used in the organization, storage, and retrieval of data and files in a database. It makes working with files easy and curbs the duplications that can arise from working with files. The capabilities that should be provided by the DBMS include;
1. A database backup and recovery system: There should be a provision for files to be backed up so as to ease their recovery when lost.
2. A good security architecture: This helps to ensure that only authorized users can get access to files. Integrity is also assured this way.
3. Concurrent access to the system: Multiple users should be able to access files at the same time.
4. Data Dictionary: This is a file that helps in the storage of information on the data in the database.
5. Data Definition: This would ensure that the structure of data is properly spelled out.
6. Data Manipulation Language: such as Sequence Query Language is a programmed language that is used in working on data and files.
Examples of DBMS software include:
MySQL, Microsoft Access, Oracle, PostgreSQL, dBase, FoxPro, etc
Hot engine oil with heat capacity rate of 4440 w/k (product of mass flow rate and specific heat) and an inlet temperature of 150°c flows through a double pipe heat exchanger. the double pipe heat exchanger is constructed of a 1.5-m-long copper pipe (k = 250 w/m·k) with an inner tube of inside diameter 2 cm and outside tube diameter of 2.25 cm. the inner diameter of the outer tube of the double pipe heat exchanger is 6 cm. oil flowing at a rate of 2 kg/s through inner tube exits the heat exchanger at a temperature of 50°c. the cold fluid, i. e., water enters the heat exchanger at 20°c and exits at 70°c. assuming the fouling factor on the oil side and water side to be 0.00015 m2 ·k/w and 0.0001 m2 ·k/w, respectively, determine the overall heat transfer coefficient on inner and outer surface of the copper tube.
Explanation:
fluid, i. e., water enters the heat exchanger at 20°c and exits at 70°c. assuming the fouling factor on the oil side and water side to be 0.00015 m2 ·k/w and 0.0001 m2 ·k/w, respectively, determine the overall heat transfer coefficient on inner and outer surface of the copper tube.xgjicbb .follow me
for a zener diode to remain in the reverse breakdown region, allowing it to maintain a constant voltage drop, the zener current must be greater than the zener knee current izk given in its datasheet. for rl
To ensure that a Zener diode remains in the reverse breakdown region and maintains a constant voltage drop, the Zener current (IZ) must be greater than the Zener knee current (IZK) specified in its datasheet. However, I'm unsure about the relevance of "rl" in your question. Could you please provide more context or clarify what "rl" refers to?
Explain the difference between dimensioning standards for inches and the standards for millimeters
Dimensioning standards for inches and millimeters are used to specify the size and location of features on an object or part. The primary difference between these two standards is the unit of measurement used.
Inches are the primary unit of measurement in the United States, and dimensioning standards for inches are based on the imperial system of measurement. This system is based on units of inches, feet, and yards.
Dimensioning standards for inches typically use fractions of an inch, such as 1/8", 1/16", or 1/32", to specify dimensions. These fractions are commonly used because they are easy to measure with common tools like rulers and calipers.
On the other hand, millimeters are the primary unit of measurement in most other parts of the world, and dimensioning standards for millimeters are based on the metric system of measurement. This system is based on units of millimeters, centimeters, and meters.
Dimensioning standards for millimeters typically use decimals, such as 1.5 mm or 3.75 mm, to specify dimensions. Decimals are commonly used in the metric system because they allow for more precise measurements and are easier to work with in mathematical calculations.
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What are the three main functions of electrical drawing
While drilling, the mud is being circulated at 2.5 bbls/minute. The surface pressure seen at the pumps is 2,500 psi.
(2 pts) Assuming the well is 7,375 ft deep, estimate is the bottomhole pressure (at 7,375 ft) under these conditions, assuming the mud weight is 11 ppg? (the bottomhole pressure is the sum of a) the surface pressure and b) the pressure caused by the column of mud in the wellbore)
The bottomhole pressure (BHP) at a given depth in a wellbore can be calculated as the sum of the hydrostatic pressure of the mud column and the surface pressure.
The hydrostatic pressure of the mud column can be calculated as:
P_hydrostatic = mud_weight * 0.052 * depth
where mud_weight is the density of the mud in pounds per gallon (ppg), 0.052 is a conversion factor to convert the mud density to psi/ft, and depth is the vertical depth of the well in feet.
In this case, the mud weight is given as 11 ppg and the well depth is 7,375 ft. Therefore, the hydrostatic pressure of the mud column is:
P_hydrostatic = 11 * 0.052 * 7375 = 4,045 psi
The surface pressure is given as 2,500 psi.
Therefore, the bottomhole pressure can be estimated as:
BHP = P_hydrostatic + surface pressure
BHP = 4,045 + 2,500 = 6,545 psi
So the estimated bottomhole pressure at 7,375 ft depth is 6,545 psi.
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A heat engine is a device able to transform work into heat.
a. True
b. False
Answer:
Option B: False
Explanation:
A heat engine is a device which operates in a manner that heat is converted into mechanical work.
A simple example of a heat engine is a drinking bird. The oscillatory motion of the drinking bird is as a result of the thermal expansion and contraction of a chemical compound in its beak, which creates an imbalance in its position of equilibrium. This causes it to oscillate.
Heat engines usually work by extracting heat once there is a temperature gradient available in the system and using it to perform work. Another good example is the internal combustion engine. It extracts heat from the explosion of the burning fuels and uses it to power the car.
______ cards provide high-quality 3-d graphics and animation for games and simulations.
Graphics cards, also known as video cards, provide high-quality 3-D graphics and animation for games and simulations. These cards are essential components of modern computers because they improve the display quality of images, videos, and animations.
More than just improving the display quality, graphics cards also help to reduce the workload on the CPU by offloading the processing of graphics to the GPU. This improves overall system performance and provides better multitasking capabilities.A typical graphics card contains a GPU (graphics processing unit), which is responsible for handling complex calculations involved in generating high-quality graphics. Texture mapping is a technique that enables the display of realistic textures, while anti-aliasing smooths out jagged edges in graphics. Shading is used to create the illusion of depth and shadows in graphics.Graphics cards are especially important for gaming because they provide smoother frame rates, better texture quality, and realistic lighting effects.
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Tony works as a Sorter in a processing factory. Which qualifications does he most likely have?
teaching skills, for helping people perform farm tasks, and creative thinking skills, for finding ways to process food
safety skills, for handling tools and food products, and honesty, for following rules and regulations
accuracy, for closely inspecting equipment and operating heavy machinery safely
accuracy, for monitoring animals, and patience and determination, for observing and caring for animals
Answer:
answer is B
Explanation:
If a water distribution system has a design population of 25,000 capita, the daily peak factor is 1.5, and the water demand from the residential area is 450 L/C/d, the required design discharge for the pumping station for the water distribution system is
Water distribution system is a structure that supplies safe and adequate water to a community. The primary requirement of the water distribution system is to meet the daily demand of the population.
The required design discharge for the pumping station for the water distribution system with a design population of 25,000 capita, the daily peak factor is 1.5, and the water demand from the residential area is 450 L/C/d is calculated as follows: Given: Design population = 25,000 capita Water demand from the
residential area = 450 L/C/d Daily peak factor = 1.5
Let's calculate the daily water demand of the community;
Daily water demand (DWD) = Design population
× water demand from residential area×
peak factor DWD = 25,000 × 450 × 1.5DWD = 16,875,000 L/day
The design discharge is calculated as;
Design discharge = Daily water demand / 24 hours
Design discharge = 16,875,000 / 24Design discharge = 703,125 L/hour
The required design discharge for the pumping station for the water distribution system is 703,125 L/hur.
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How often should a technician conduct a Quality Inspection?
Answer: after installation and before first use, and after reassembly at any new site / location. And at suitable intervals to make sure no problems have surfaced.
Assume that you have a direct-mapped cache with 16 indexes and each block can contain 16 words. Assuming that an address is 32 bits.
How many bits in each 32bit address are used for its tag?
There are no bits left for the tag in a direct-mapped cache with 16 indexes, each block can contain 16 words and with an address of 32 bits.
Given a direct-mapped cache with 16 indexes and each block can contain 16 words. An address is 32 bits. We need to calculate the number of bits used for the tag. Here is the calculation:First, we find the number of bits needed for each block by dividing the number of words in each block (16) by the size of a word in bits. As given, the size of a word is not given in the question, we will assume it as 2 bytes which is equal to 16 bits. Size of block = 16 × 16 = 256 bits.
Number of blocks = 2^(32-4-4-8) = 2^16Number of indexes = 16Index bits = log2 16 = 4 bits Index size = 4 bits × 16 blocks = 64 bits Now, to find the number of bits used for its tag, we will subtract the number of bits needed for the index and block from the total number of bits in the address. Tag bits = 32 - 64 - 256 = -288 bits This doesn't make sense. In a direct-mapped cache with the given specifications, there is no space for the tag in a 32-bit address.
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Help I need fast is it true or false
Answer:
False
Explanation:
It can only survive outside of the body for six days
how can you obtain the pressure altitude on flights below 18,000 feet?
To obtain the pressure altitude on flights below 18,000 feet, pilots can set the altimeter to the standard pressure setting of 29.92 inches of mercury (inHg) and read the indicated altitude.
Pressure altitude is the altitude above the standard atmospheric pressure level. It is an important reference for pilots to determine the aircraft's height above the ground and to comply with altitude restrictions. When flying below 18,000 feet, pilots can obtain the pressure altitude by following these steps:
Set the altimeter: The altimeter should be set to the standard pressure setting of 29.92 inHg. This compensates for variations in atmospheric pressure and provides a common reference for all aircraft.
Read the indicated altitude: Once the altimeter is set to the standard pressure, pilots can read the indicated altitude displayed on the altimeter. This reading represents the pressure altitude, which is the height above the standard atmospheric pressure level.
By setting the altimeter to the standard pressure and reading the indicated altitude, pilots can determine the pressure altitude during flights below 18,000 feet. It is important for pilots to continually adjust their altimeters as they encounter changes in atmospheric pressure during the flight to maintain accurate altitude references and ensure safe operations.
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Give an example of one technology that is well matched to the needs of the environment, and one technology that is not.
Answer:
oh god... i have no idea lm.ao
Explanation:
gross combination weight rating (gcwr) means the value specified by the manufacturer as the loaded weight of a single vehicle. group of answer choices true false
False.
The Gross Combination Weight Rating (GCWR) is not the loaded weight of a single vehicle specified by the manufacturer. It is the maximum allowable combined weight of a towing vehicle (GVWR) and its trailer.What is Gross Combination Weight Rating (GCWR)?The maximum allowable weight of a fully-loaded towing vehicle (GVWR) and its loaded trailer is known as the Gross Combination Weight Rating (GCWR). A truck's GCWR specifies the maximum weight that the truck can carry and the maximum weight that the truck can tow when attached to a trailer. The GCWR is calculated by adding the towing vehicle's GVWR and the loaded weight of the trailer. That is, GCWR = GVWR + loaded weight of the trailer.
The GVWR of a vehicle is the maximum weight that the vehicle can carry, including the weight of the vehicle, passengers, cargo, and fuel. In contrast, the loaded weight of the trailer is the sum of the weight of the trailer, its cargo, and any other accessories. When you exceed the GCWR, the truck becomes harder to handle and less safe, so it's crucial to know your GCWR before towing a trailer.
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forces of 300 lb and 600 lb act on a machine part at angles of 45 and -30 respectively with the x axis. True or false
Since the x-components of the forces add up to a value greater than zero, the statement "forces of 300 lb and 600 lb act on a machine part at angles of 45 and -30 respectively with the x-axis" is FALSE. The net x-component of the forces is approximately 730.5 lb.
To determine if this statement is true or false, we can use vector addition.
Force 1: 300 lb at an angle of 45 degrees with the x-axis.
Force 2: 600 lb at an angle of -30 degrees with the x-axis.
To find the x-component of a force, we use the formula:
Fx = F cos θ
where:
F is the magnitude of the force, and
θ is the angle with the x-axis.
Then , let's calculate the x-components of the forces:
For force 1:
F1x = 300 lb x cos 45°
F1x = 150√2 lb
For force 2:
F1x = 600 lb x cos -(-30)°
F1x = 300√3 lb
Now, since both forces are acting along the x-axis, we can add their x-components:
Total x-component of forces = F1x + f2x = 150√2 lb + 300√3 lb
To determine whether the sum of these x-components is 0 or not, we need to calculate the numeric value.
F1x + f2x ≈ 150 x 1.41 + 300 x 1.73
F1x + f2x ≈ 211.5 +519
F1x + f2x ≈ 730.5 lb
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Which of the following workers are not likely to be paid during an election?
campaign press secretary
volunteer coordinator
poll worker
director of communications
Answer:
volunteer coordinator
Explanation:
because they are volunteering for that and in most of the cases they do not expect to be paid
Question Is in the image provided
The two ways through which a computer model is likely to be used by an engineer in order to help refine a design are as follows:
Calculating the possible costs of building a design.Running simulations to test a problem with the design.Thus, the correct options for this question are A and D.
What do you mean by Computer model?A Computer model may be defined as a type of computer program that significantly runs on a computer that typically develops a model, or simulation, of a real-world feature, phenomenon, or any other event.
According to the context of this question, an engineer would try to perform the ways in order to support the refining of the design through the help of calculating the possible costs of building a design and the run simulations to test a problem with the design.
Therefore, the correct options for this question are A and D.
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#5 Air undergoes an adiabatic compression in a piston-cylinder assembly from P1= 1 atm and Ti=70 oF to P2= 5 atm. Employing ideal gas model with constant specific heat capacity ratio (Y), determine the work and heat transfer per unit mass if y = 1.5. (15 points)
Answer:
The work transfer per unit mass is approximately 149.89 kJ
The heat transfer for an adiabatic process = 0
Explanation:
The given information are;
P₁ = 1 atm
T₁ = 70°F = 294.2611 F
P₂ = 5 atm
γ = 1.5
Therefore, we have for adiabatic system under compression
\(T_{2} = T_{1}\cdot \left (\dfrac{P_{2}}{P_{1}} \right )^{\dfrac{\gamma -1}{\gamma }}\)
Therefore, we have;
\(T_{2} = 294.2611 \times \left (\dfrac{5}{1} \right )^{\dfrac{1.5 -1}{1.5 }} \approx 503.179 \ K\)
The p·dV work is given as follows;
\(p \cdot dV = m \cdot c_v \cdot (T_2 - T_1)\)
Therefore, we have;
Taking air as a diatomic gas, we have;
\(C_v = \dfrac{5\times R}{2} = \dfrac{5\times 8.314}{2} = 20.785 \ J/(mol \cdot K)\)
The molar mass of air = 28.97 g/mol
Therefore, we have
\(c_v = \dfrac{C_v}{Molar \ mass} = \dfrac{20.785}{28.97} \approx 0.7175 \ kJ/(kg \cdot K)\)
The work done per unit mass of gas is therefore;
\(p \cdot dV =W = 1 \times 0.7175 \times (503.179 - 294.2611) \approx 149.89 \ kJ\)
The work transfer per unit mass ≈ 149.89 kJ
The heat transfer for an adiabatic process = 0.
This list gives the lengths of different leaves in centimeters. 7. 5, 9. 5, 9. 0, 8. 0, 7. 5, 8. 5, 7. 5, 8. 5, 9. 5, 8. 5, 9. 0, 9. 5, 8. 0, 9. 5, 8. 0, 9. 0, 9. 0, 9. 0 Create a line plot to display the data. To create a line plot, hover over each number on the number line. Then click and drag up to plot the data
The line plot would have a number line ranging from 7 to 9.5 with increments of 0.5. There would be data points plotted at 7.5, 9.5, 9.0, 8.0, 8.5, and 9.0, with multiple points at certain values.
The line plot would visually represent the distribution of leaf lengths.
Here is a textual representation of the line plot based on the given data:
7.5 | X
7.75 |
8.0 | X
8.25 |
8.5 | X X
8.75 |
9.0 | X X X X
9.25 |
9.5 | X X X
9.75 |
In the line plot, each X represents a data point from the given list. The vertical axis represents the count or frequency of each length, while the horizontal axis represents the range of lengths.
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if the height of a 12 in. wide rectangular beam section is increased from 16 in. to 32 in. (i.e., initial section is 12x16 in. and final section is 12x32 in.), the maximum flexure or bending stress in the beam becomes?
The maximum flexure or bending stress in the beam is increased by a factor of 4.
The maximum flexure or bending stress in a beam is calculated using the equation:
σ = Mc/I
Where,
σ = Maximum flexure or bending stress (MPa)
M = Maximum bending moment (N.m)
c = Distance from Neutral Axis to outermost fibre (mm)
I = Moment of Inertia (mm4)
For the given beam,
Initial Section: 12 x 16 in.
Final Section: 12 x 32 in.
For the initial section:
I1 = b1 x h12^3/12 = 12 x 162^3/12 = 24576 in4
For the final section:
I2 = b2 x h22^3/12 = 12 x 322^3/12 = 98304 in4
Therefore, the Moment of Inertia (I) is increased by a factor of 4 (I2 = 4 x I1).
Since M and c remain unchanged, the maximum flexure or bending stress (σ) is increased by a factor of 4 (σ2 = 4 x σ1).
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Select the lightest wide flange steel section for simple beam of 10 m span that will carry a uniform load of 20 kN/m. Use A36 and assume that the beam is supported laterally for its entire length. [Hint: V max = wL/2; Mmax = wL2/8, Minimum yield stress for A36=250MPa.]
The lightest wide flange steel section that can be used is W250x73. This means it is a wide flange beam with a weight of 73 kg/m and a nominal depth of 250 mm.
The maximum shear force (Vmax) and maximum bending moment (Mmax) in a basic beam with a 10 m span and a uniform load of 20 kN/m must be taken into account in order to calculate the lightest wide flange steel section.
Here it is given that:
Span length (L) = 10 m
Uniform load (w) = 20 kN/m
Minimum yield stress for A36 steel = 250 MPa
We know that:
Vmax = wL/2
Mmax = \(wL^2/8\)
Vmax = (20 kN/m) * (10 m) / 2
Vmax = 100 kN
Mmax = (20 kN/m) * (10 m)^2 / 8
Mmax = 250 kNm
The lightest wide flange steel section that can be used is W250x73, according to calculations and steel section tables.
Thus, this indicates that the beam has a wide flange, weighs 73 kg/m, and has a nominal depth of 250 mm.
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Assume that words has been initialized with one or more strings containing only lowercase letters. Which of the following code segments can be used to replace /* missing implementation */ so that findLastWord will work as intended?
A. int maxIndex = 0;
for (int k = 0; k < words.length; k++)
{if (words[k].compareTo(maxIndex) > 0){maxIndex = k;}}return words[maxIndex];
B. int maxIndex = 0;for (int k = 1; k <= words.length; k++){if (words[k].compareTo(words[maxIndex]) > 0){maxIndex = k;}}
return words[maxIndex];
C. int maxIndex = 0;
for (int k = 1; k < words.length; k++){if (words[k].compareTo(words[maxIndex]) > 0){maxIndex = k;}}
return maxIndex;
D. String maxWord = words[0];for (int k = 1; k < words.length; k++){if (words[k].compareTo(maxWord) > 0){maxWord = k;}}
return maxWord;
E. String maxWord = words[0];for (int k = 1; k < words.length; k++){if (words[k].compareTo(maxWord) > 0){maxWord = words[k];}}
return maxWord;
Code segment E can be used to replace /* missing implementation */ so that `findLastWord` will work as intended. In the `findLastWord` function, the goal is to find the word with the highest lexicographic order (i.e., the last word in alphabetical order). Let's analyze each code segment to determine which one correctly implements this logic.
A: This code segment is incorrect because `compareTo` expects a `String` argument, but `maxIndex` is an integer. Additionally, it compares the word with an index instead of comparing words directly.
B: This code segment is almost correct. However, the loop condition `k <= words.length` is incorrect because array indices start from 0. It should be `k < words.length`.
C: This code segment is incorrect because it returns the index of the word with the highest lexicographic order instead of the word itself.
D: This code segment is incorrect because it compares words using `compareTo` but assigns the index `k` to `maxWord` instead of the word itself.
E: This code segment is correct. It initializes `maxWord` with the first word in the array and iterates over the remaining words. It compares each word to `maxWord` using `compareTo` and updates `maxWord` if a word with a higher lexicographic order is found. Finally, it returns the word stored in `maxWord`, which will be the last word in alphabetical order. Therefore, code segment E is the correct choice to replace /* missing implementation */.
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(a) (6 points) Find the integer a in {0, 1,..., 26} such that a = -15 (mod 27). Explain. (b) (6 points) Which positive integers less than 12 are relatively prime to 12?
a. a = 12 is the solution to the given congruence relation. b. the positive integers less than 12 that are relatively prime to 12 are 1, 5, 7, and 11.
(a) The main answer: The integer a that satisfies a ≡ -15 (mod 27) is 12.
To find the value of a, we need to consider the congruence relation a ≡ -15 (mod 27). This means that a and -15 have the same remainder when divided by 27.
To determine the value of a, we can add multiples of 27 to -15 until we find a number that falls within the range of {0, 1,..., 26}. By adding 27 to -15, we get 12. Therefore, a = 12 is the solution to the given congruence relation.
(b) The main answer: The positive integers less than 12 that are relatively prime to 12 are 1, 5, 7, and 11.
Supporting explanation: Two integers are relatively prime if their greatest common divisor (GCD) is 1. In this case, we are looking for positive integers that have no common factors with 12 other than 1.
To determine which numbers satisfy this condition, we can examine each positive integer less than 12 and calculate its GCD with 12.
For 1, the GCD(1, 12) = 1, which means it is relatively prime to 12.
For 2, the GCD(2, 12) = 2, so it is not relatively prime to 12.
For 3, the GCD(3, 12) = 3, so it is not relatively prime to 12.
For 4, the GCD(4, 12) = 4, so it is not relatively prime to 12.
For 5, the GCD(5, 12) = 1, which means it is relatively prime to 12.
For 6, the GCD(6, 12) = 6, so it is not relatively prime to 12.
For 7, the GCD(7, 12) = 1, which means it is relatively prime to 12.
For 8, the GCD(8, 12) = 4, so it is not relatively prime to 12.
For 9, the GCD(9, 12) = 3, so it is not relatively prime to 12.
For 10, the GCD(10, 12) = 2, so it is not relatively prime to 12.
For 11, the GCD(11, 12) = 1, which means it is relatively prime to 12.
Therefore, the positive integers less than 12 that are relatively prime to 12 are 1, 5, 7, and 11.
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Determine the critical load if the bottom is fixed and the top is pinned. ewew = 1. 6 ×(10)3ksi×(10)3ksi ,σyσy = 5 ksiksi
Critical load Fcr or buckling load is the value of load that causes the phenomenon of change from stable to unstable equilibrium state.
With that beign said, first it is neessary to calculate the moment of inercia about the x-axis:
\(Ix= \frac{db^3}{12}\\ Ix = \frac{2.(4)^3}{12} = 10.667in\)
Then it is necessary to calculate the moment of inercia about the y-axis:
\(Iy = \frac{db^3}{12}\\ Iy = \frac{4.(2)^3}{12} = 2.662in\)
Comparing both moments of inercia it is possible to assume that the minimun moment of inercia is the y-axis, so the minimun moment of inercia is 2662in.
And so, it is possible to calculate the critical load:
\(Pc\gamma = \frac{2046\pi ^2E.I}{L^2} \\Pc\gamma= \frac{2046.\pi ^2.(1,6.10^3.10^3).2662}{(10.12)^2} \\Pc\gamma= 5983,9db\)
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