A simply supported wood beam AB with span length L = 4 m carries a uniform load of intensity q = 8.8 kN/m(see figure).
(a) Calculate the maximum bending stress σmax due to the load q if the beam has a rectangular cross section with width b = 140 mm and height h = 240 mm. (b) Repeat part (a) but use the trapezoidal distributed load shown in the figure part b.
Answers
The maximum bending stress due to the trapezoidal load is 0.637 MPa.
(a) Calculation of maximum bending stress due to uniform load:
The maximum bending stress in a simply supported beam due to a uniform load is given by:
σmax = (5/384) * (q * L^4) / (I * 10^6)
where q is the uniform load, L is the span length, I is the moment of inertia of the cross section of the beam, and σmax is the maximum bending stress.
The moment of inertia of a rectangular cross section about its neutral axis is given by:
I = (bh^3) / 12
where b is the width and h is the height of the cross section.
Substituting the given values of q, L, b, and h, we get:
I = (140 * 240^3) / 12 = 58,752,000 mm^4
σmax = (5/384) * (8.8 * 4^4) / (58,752,000 * 10^6) = 0.262 MPa
Therefore, the maximum bending stress due to the uniform load is 0.262 MPa.
(b) Calculation of maximum bending stress due to trapezoidal load:
For a trapezoidal load, the maximum bending stress occurs at the mid-span of the beam and is given by:
σmax = (3/16) * (q * L) * (h / (2 * I * 10^6)) * (4h/3)
where q is the maximum load intensity, L is the span length, h is the height of the beam, and I is the moment of inertia of the cross section of the beam.
The maximum load intensity q can be found by calculating the average load intensity over the length of the beam, which is given by:
q = (2 * q1 + q2) / 3
where q1 is the load intensity at the support and q2 is the load intensity at the mid-span of the beam.
Substituting the given values of q1, q2, L, b, and h, we get:
q = (2 * 0 + 8.8) / 3 = 2.933 kN/m
I = (140 * 240^3) / 12 = 58,752,000 mm^4
Substituting these values into the equation for maximum bending stress, we get:
σmax = (3/16) * (2.933 * 4) * (240 / (2 * 58,752,000 * 10^6)) * (4/3 * 240) = 0.637 MPa
Click the below link, to learn more about the trapezoidal :
https://brainly.com/question/3905212
#SPJ11
Related Questions
the perimeter of a pool table is 30ft. The table is twice as long as it is wide. What is the length of the pool table?
Answers
10 ft pls like if it helped
whats the equation for the table
Answers
Answer:
y= 32x
Step-by-step explanation:
Use slope formula
192-128/6-4= 64/2
M=32x
Find y-intercept (if any)
128=32(4)+b
128=128+b
B=0
1. If f(x) = (3x-2)/(2x+3), then f'(x) =
Answers
Answer:
\(f'(x)= \frac{13}{(2x+3)^2}\\\)
Step-by-step explanation:
\(f(x)= \frac{3x-2}{2x+3} \\\)
\(f'(x)=\frac{dy}{dx} = \frac{d}{dx}(\frac{3x-2}{2x+3})\\ f'(x)= \frac{(2x+3)\frac{d}{dx}(3x-2)-(3x-2)\frac{d}{dx}(2x+3) }{(2x+3)^{2} } \\f'(x)= \frac{(2x+3)(3)-(3x-2)(2)}{(2x+3)^{2} } \\\)
\(f'(x)= \frac{6x+9-6x+4}{(2x+3)^{2} }\\ f'(x)= \frac{13}{(2x+3)^2}\\\)
What is an angle that is supplementary to
Answers
Answer: Please check below
Step-by-step explanation:
So we know that a supplementary angle is always 180 degree angle. 180 is basically a straight angle. So DEB is a straight line. Due to this we can tell that one of the supplementary angles could be DEC. Thank you!
Note: There are many solutions but DEB is one of them.
The following are the annual operations. The interest rate for the first fourteen years is 1% per month and thereafter will be 1.5% per month: $100,000 will be contributed at the end of each year for 8 years. end of each year for 8 years (the first is at the end of year 1); equal annual withdrawals will be made from the end of year 10 to the end of year 14 of $60,000; finally, equal contributions of $50,000 will be made from the end of year 15 to the end of year 20.
8. Calculate the effective annual interest rates: Answer 12.6825% and 19.56182%.
9. Calculate the balance in present value: Answer $444,117.28
10. Calculate the balance in future value: Answer $6,903,087.93
Answers
Effective annual interest rates: 12.6825% for the first 14 years, 19.56182% thereafter.
Balance in present value: $444,117.28.
Balance in future value: $6,903,087.93.
The effective annual interest rates for the given operations are 12.6825% for the first 14 years and 19.56182% thereafter. These rates take into account compounding on a monthly basis and reflect the actual annual return on the investments.
To calculate the effective annual interest rate for the first 14 years, we can use the formula: (1+monthly interest rate)12−1(1+monthly interest rate)12−1. Plugging in the monthly interest rate of 1%, we find that the effective annual interest rate is 12.6825%.
For the period after 14 years, the effective annual interest rate can be calculated using the same formula, but with the monthly interest rate of 1.5%. Substituting this value, we obtain an effective annual interest rate of 19.56182%.
The balance in present value can be calculated as the sum of the present values of the contributions and withdrawals. The present value of a cash flow can be calculated using the formula: FV(1+r)n(1+r)nFV, where FV is the future value, r is the interest rate, and n is the number of periods.
To calculate the balance in present value, we need to determine the present value of the contributions, withdrawals, and future contributions. Applying the formula for each cash flow and summing them up, we find that the balance in present value is $444,117.28.
The balance in future value can be calculated as the sum of the future values of the contributions and withdrawals. The future value of a cash flow can be calculated using the formula: PV×(1+r)nPV×(1+r)n, where PV is the present value, r is the interest rate, and n is the number of periods.
To calculate the balance in future value, we need to determine the future value of the contributions, withdrawals, and future contributions. Applying the formula for each cash flow and summing them up, we find that the balance in future value is $6,903,087.93.
learn more about "interest ":- https://brainly.com/question/25720319
#SPJ11
a square with a side length of 5 inches has a area of 25 in
true or false
Answers
Answer:
TRUE
Step-by-step explanation:
5 x 5 = 25 in²
simplify (1-cos x)(1+cos x)
Answers
Answer:
\(sin^2x\)
Step-by-step explanation:
To simplify the expression (1 - cos x)(1 + cos x), we can use the difference of squares identity, which states that \(a^2 - b^2 = (a + b)(a - b).\)
Let's apply this identity to the given expression:
\((1 - cos x)(1 + cos x) = 1^2 - (cos x)^2\)
Now, we can simplify further by using the trigonometric identity \(cos^2(x) + sin^2(x) = 1.\) By rearranging this identity, we have \(cos^2(x) = 1 - sin^2(x).\)
Substituting this into our expression, we get:
\(1^2 - (cos x)^2 = 1 - (1 - sin^2(x))\)
Simplifying further:
\(1 - (1 - sin^2(x)) = 1 - 1 + sin^2(x)\)
Finally, we get the simplified expression:
\((1 - cos x)(1 + cos x) = sin^2(x)\)
To simplify the expression \(\sf\:(1-\cos x)(1+\cos x)\\\), follow these steps:
Step 1: Apply the distributive property.
\(\longrightarrow\sf\:(1-\cos x)(1+\cos x) = 1 \cdot 1 + 1 \cdot \\\)\(\sf\: \cos x -\cos x \cdot 1 - \cos x \cdot \cos x\\\)
Step 2: Simplify the terms.
\(\longrightarrow\sf\:1 + \cos x - \cos x - \cos^2 x\\\)
Step 3: Combine like terms.
\(\longrightarrow\sf\:1 - \cos^2 x\\\)
Step 4: Apply the identity \(\sf\:\cos^2 x = 1 - \sin^2 x\\\).
\(\sf\:1 - (1 - \sin^2 x)\\\)
Step 5: Simplify further.
\(\longrightarrow\sf\:1 - 1 + \sin^2 x\\\)
Step 6: Final result.
\(\sf\red\bigstar{\boxed{\sin^2 x}}\\\)
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
What is the volume of this figure?
Enter your answer in the box.
yd³
Answers
Answer:
4095
Step-by-step explanation:
This Is for the 4.07 K-12 Quiz! <3
Answer:
4095 yd³ for K12
an economist wondered if people who go grocery shopping on weekdays go more or less often on fridays than any other day. she figured that if it were truly random, 20% of these shoppers would go grocery shopping on fridays. she randomly sampled 75 consumers who go grocery shopping on weekdays and asked them on which day they shop most frequently. of those sampled, 24 indicated that they shop on fridays more often than other days. the economist conducts a one-proportion hypothesis test at the 1% significance level, to test whether the true proportion of weekday grocery shoppers who go most frequently on fridays is different from 20%. (a) which answer choice shows the correct null and alternative hypotheses for this test?
Answers
The true percentage of grocery shoppers that shop most frequently on Fridays from Monday to Friday, which is 20%, cannot be determined statistically. The value of p is 0.0130.
To solve this problem, we run a hypothesis test about the population proportion.
Proportion in the null hypothesis (p0) = 0.2
Sample size (n) = 75
Sample proportion (sp) = 24/75 = 0.32
Significance level = 0.01
\(H_{o}\) : p = 0.2
\(H_{a}\) : p ≠ 0.2
Test statistic percentage = ( \(sp\) - \(p_{o}\) ) / \(\sqrt{\frac{(p_{o})(1-p_{o} )}{n} }\)
Left critical \(z_{0.01}\) = -2.5758
Right critical \(z_{0.01}\) = 2.5758
Calculated statistic = \(\frac{0.32-0.2}{\sqrt{\frac{(0.32)(1-0.32)}{75} } }\) = 2.2278
Since, -2.5758 < Test statistic < 2.5758, the null hypothesis cannot be rejected. There is not enough statistical evidence to state that the true proportion of grocery shoppers from Monday to Friday that goes most frequently on Fridays is different from 20%. The p - value is 0.0130.
Therefore,
The true percentage of grocery shoppers that shop most frequently on Fridays from Monday to Friday, which is 20%, cannot be determined statistically. The value of p is 0.0130.
To learn more about Percentage visit :
brainly.com/question/14869182
#SPJ4
the bottom sides of two similar triangles are_______ sides
Answers
Answer: Proportional
Step-by-step explanation: When to corresponding sides of different triangles are alike, they are considered to be proportional.
Stella has $4.50 worth of dimes and quarters. She has 3 more dimes than quarters. Determine the number of dimes and the number of quarters that Stella has.
Answers
Answer:
12 quarters, 15 dimes
Step-by-step explanation:
Let q be the number of quarters and d be the number of dimes. We set up and solve this system of equations:
.10d + .25q = 4.50
d = 3 + q
.10(3 + q) + .25q = 4.50
.30 + .10q + .25q = 4.50
.30 + .35q = 4.50
.35q = 4.20
q = 12, d = 15
Ryan and Carlos are getting in shape for football season. Ryan starts at 140 pounds and gains two pounds per week. Carlos starts at 195 pounds but
loses three pounds per week. In how many weeks will they both weigh the same amount, and what will that weight be? (Hint: these are y = equations)
Answers
Answer:
In 11 weeks they will both be 162lbs each
Step-by-step explanation:
two numbers are in the ratio 5:3.if they deffer by 18,what are the numbers?
Answers
Answer:
let common ratio between them be x
So, 5x,3x
5x-3x=18
2x=18
2x/2=18/2
x=9
Step-by-step explanation:
I hope it helps you☺️
If yes, do mark my answer as brainliest
can someone help me out with this question, please!?!
state if the three sides lengths form a right triangle.
1.
\( \sqrt{143} \)
\( \sqrt{87} \)
15
2.
\( \sqrt{10} \)
1
\( \sqrt{11} \)
Answers
The three sides lengths √143, √87 and 15 does not form a right triangle.
The three sides lengths √10, √11 and 1 forms a right triangle.
What is Pythagorean theorem?In Euclidean geometry, Pythagorean's theorem is given by this mathematical expression:
a² + b² = c²
Where:
a, b, and c represents the side lengths of a right-angled triangle.
In order for the segments connecting the given points to form a right-angled triangle, its side lengths must satisfy the Pythagorean's theorem:
a² + b² = c²
(√87)² + (√143)² = 15²
87 + 143 = 225
230 = 225 (False).
a² + b² = c²
1² + (√10)² = (√11)²
1 + 10 = 11
11 = 11 (True).
Read more on Pythagorean theorem here: brainly.com/question/23200848
#SPJ1
If y varies directly as x and inversely as z and y = 4 when x = 2 and z = 7, find y when x =
6 and z = 3.
Answers
Answer:
y = 28
Step-by-step explanation:
Given that y varies directly as x and inversely as z then the equation relating them is
y = \(\frac{kx}{z}\) ← k is the constant of variation
To find k use the condition y = 4 when x = 2 and z = 7, then
4 = \(\frac{2k}{7}\) ( multiply both sides by 7 )
28 = 2k ( divide both sides by 2 )
14 = k
y = \(\frac{14x}{z}\) ← equation of variation
When x = 6 and z = 3 , then
y = \(\frac{14(6)}{3}\) = 14 × 2 = 28
Write an equation of a line in point-slope form with the
information given.
1. passes through: (6, 0); slope: - 1/6
Answers
Answer: (y − 0) = -(1/6)(x − 6) or y=-(1/6)(x-6)
Step-by-step explanation:
An equation in Point Slope form: y − y1 = m(x − x1), where m is the slope and x1 and y1 are provided as a single point, (x1,y1). We have slope(m) = -(1/6) and are given (6,0). Therefore:
(y − 0) = -(1/6)(x − 6) (Point slope form)
y = -(1/6)(x-6)
Rewriting this into standard form, y = mx + b
y = -(1/6)x + 1
Hell I’ll mark brainlest!
Answers
Answer:
Read answer below :)
Step-by-step explanation:
So you know that the height is 12 cm, and the base is 27 cm at full. When they show you half, that's 13.5. So, having three sides in the entire base-length of 27 cms, you'll divide 27 by 3, in which case you get 9. Each the the base lengths are 9.
So the formula for volume is length * width * height. Knowing the width (13.5), the length (9), and height (12), multiply them. Your final answer is 1458 for all of it. For one side, divide by 6.
Hope this helps
Ziyad has a rectangular swimming pool in his backyard as shown below.
a) Write a polynomial in simplest terms that represents the amount of water this pool can hold (Volume).
B) find the volume If x = 2 feet
Answers
Answer:
A) V(x) = x(8x - 4)(2.5x)
B) V(2) = 3(8(2) - 4)(2.5(2)) = 3(12)(5)
= 180 cubic feet
In the given figure,
Length = 8x - 4
Breadth = 2.5 x
height = x
(a)
Write a polynomial in simplest term that represents the amount of water this pool can hold (volume)
We can see that the shape of the pool is cuboid.
Volume of cuboid = LBH
Volume = (8x - 4)(2.5x)(x)
(b) Find the volume if x = 2 feet.
Length of pool = 8x - 4
8(2) - 4
16 - 4 = 12 feet
Breadth of pool = 2.5x
2.5 × 2 = 5 feet
Now,
Volume = LBH
Volume = 12 × 5 × 2
Volume = 60 × 2
Volume = 120 cubic feet.
Hence Volume of the pool = 120 cubic feet
Take the equation 103=-7(x+8)+7(x+7). Jamie says this equation has no solution. Mick says it does. Who is correct? Why?
Answers
\( 👋 \) Hello ! ☺️
Step-by-step explanation:
\( 103 = - 7(x + 8) + 7(x + 7) \)
\( 103 = - 7x - 56 + 7x + 49 = 0x + 7 \)
0x= 7 => x ∉ |R
\(\boxed{\color{gold}{S = ∅}} \)
Jamie is right.
* Any number multiplied by 0 gives 0.
Which equation represents a line that passes through (-9, -3) and has a slope of -6? - = y-9 = -6(x-3) y + 9 = -6(x + 3) y-3 = -6(x-9) O y + 3 = -6(x + 9) = x
Answers
Answer:
(y+3)=−6(x+9) ( y + 3 ) = − 6 ( x + 9 )
Step-by-step explanation:
A cone has the same height of 13 of the radius of the original cone. Complete the expression for its volume.
Answers
The volume of the cone with a height of 13 times the radius of the original cone can be expressed as V = (1/3)πr^2(13r), where r is the radius.
The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius and h is the height. In this case, the height of the new cone is 13 times the radius of the original cone.
Therefore, we can replace the height, h, with 13r, where r is the radius. Substituting this into the volume formula, we get V = (1/3)πr^2(13r).
This expression represents the volume of the cone with a height of 13 times the radius of the original cone. By plugging in the value of the radius, we can calculate the actual volume of the cone.
Learn more about Expression click here :brainly.com/question/24734894
#SPJ11
please help ٩(๑òωó๑)۶
Answers
Answer:
Height of the cliff = 13.66 m
Step-by-step explanation:
Let the height of the cliff is 'x' m and distance between the base of the cliff and the boat is 'y' m.
From right triangle AOC,
tan 30° = \(\frac{\text{Opposite triangle}}{\text{Adjacent side}}\)
\(\frac{1}{\sqrt{3}}=\frac{x}{y}\)
y = \(x\sqrt{3}\) ------(1)
From right angle triangle BOC,
tan 45° = \(\frac{x}{y-10}\)
\(1=\frac{x}{y-10}\)
x = y - 10
y = x + 10 -------(2)
From equations (1) and (2),
\(x\sqrt{3}=x+10\)
\(x(\sqrt{3}-1)=10\)
\(x=\frac{10}{\sqrt{3}-1 }\)
x = 13.66 m
Therefore, height of the cliff is 13.66 m.
(8,12) and (x,9) where m = -1/2
Answers
Answer:
Step-by-step explanation:
The slope of a line between two points (x1, y1) and (x2, y2) is given by:
m = (y2 - y1) / (x2 - x1)
In this case, we are given that m = -1/2, so substituting in the two points we have:
-1/2 = (9 - 12) / (x - 8)
Expanding and simplifying the equation:
-1/2 = -3 / (x - 8)
Multiplying both sides by -2:
1 = 3 / (x - 8)
Multiplying both sides by (x - 8):
x - 8 = 3
Adding 8 to both sides:
x = 11
So the x-coordinate of the second point is x = 11.
Find the 5 number summary for the data shown 5 number summary:
Answers
The five number summary of the given data is the minimum value = 20, maximum value = 100, median = 69.5, Q1 = 48, and Q3 = 89.
A number summary consists of five values: the most extreme values in the data set (the maximum and minimum values), the lower and upper quartiles, and the median. In order to find the five number summary,
1. Arrange the given data in ascending order. In the given case, the data is already in ascending order.
2. Determine the minimum and maximum value for the data set. In the given case, the minimum value is 20 and maximum value is 100.
3. Determine the median of the data set. The median refers to the middle number of the data set. If the data is an even set of numbers, the middle two terms are averaged. In the given case, there are 14 numbers, hence the median is an average of 7th and 8th term.
Median = (69 + 70)/2 = 69.5
4. Determine the lower quartile (Q1) and upper quartile (Q3). The Q1 and Q3 are the middle term of the lower and upper range respectively.
For the lower range, 20, 33, 43, 48, 64, 68, 69, the middle term is 48. Hence Q1 = 48.
For the upper range, 70, 72, 83, 89, 96, 99, 100, the middle term is 89. Hence Q3 = 89.
Note: The question is incomplete. The complete question probably is: Find the 5 number summary for the data shown. 20, 33, 43, 48, 64, 68, 69, 70, 72, 83, 89, 96, 99, 100
Learn more about Number summary:
https://brainly.com/question/17076973
#SPJ4
The amount a babysitter charges for babysitting services per hour is shown in the table below. What is the rate of change and what does it represent? What is the y Intercept and what does it represent?
Answers
Answer:
y=8x+2
Step-by-step explanation:
the slope is 8 and the y intercept is 2
the slope is 8 dollars the increase of the price per hour. the yintercept is the amount she get for 0 hours (2 dollars)
1,10
2,18
8/1 is 8
10=8*1+b
10=8+b
2=b
Use the quadratic model y=-4x^2-3x+4 to predict y if x equals 5
Answers
Answer:
y = -4x^2 - 3x + 4
x = 5
y = -4(5)^2 - 3(5) + 4
y = -4(25) - 15 + 4
y = -100 - 15 + 4
y = -114
Step-by-step explanation:
PLEASE HELP ! :)
1. G(X)=1/4x+1
what is g(-16)?
g(-16)=
Answers
In many cases, when we evaluate functions, we just have to replace x with a given value and simplify the expression.
Solving the Question\(g(x)=\dfrac{1}{4}x+1\)
⇒ To solve for g(-16), plug in -16 as x:
\(g(x)=\dfrac{1}{4}(-16)+1\\\\g(x)=-4+1\\\\g(x)=-3\)
Answerg(-16) = -3
the slope of the line tangent to the graph of y=xe^x at x=ln 2 is
Answers
Answer:
2 + 2 ㏑2
Step-by-step explanation:
y = x (e^x)
to dy/dx (slope), we need to perform the product rule:
if y = f(x) g(x), where both f(x) and g(x) are functions in x, then dy/dx = f(x) g'(x) + f'(x) g(x).
let u = x (dy/dx = 1) and v = e^x ( dv/dx = e^x).
then dy/dx = u (dv/dx) + v (du/dx)
= x (e^x) + e^x. this is the slope.
at x = ㏑2:
dy/dx = ㏑2 (e^㏑2) + e^㏑2
= ㏑2 (2) + 2
= 2 + 2 ㏑2
James owns a restaurant and has 216 two-liter
bottles of soda to use for the soda machines, but wants to save space by pouring all the soda into one-gallon jugs. How many jugs does James need to hold all of the soda? Round your answer to three decimal
places, if necessary. Use 1 gal = 3. 785 L
Answers
In this case, 114.098 rounds up to 115 when rounded to the nearest whole number. Thus, James needs 115 one-gallon jugs to hold all of the soda.
To find the total volume of soda in gallons, we first need to convert the total volume of soda from liters to gallons. We can use the conversion factor 1 gal = 3.785 L.
So, we start by multiplying the number of 2-liter bottles by 2 to get the total volume of soda in liters:
216 x 2L = 432 L
Then, we can convert this value to gallons by dividing by the conversion factor:
432 L / 3.785 L/gal = 114.098 gal
Since we can't have a fraction of a jug, we need to round up to the nearest whole number of jugs. In this case, 114.098 rounds up to 115 when rounded to the nearest whole number.
Therefore, James needs 115 one-gallon jugs to hold all of the soda.
To learn more about volume Click here:
brainly.com/question/1578538
#SPJ4
A 120
B 20
C 160
D 170
Answers
Answer:
D
Step-by-step explanation:
it points at 170 so itsD