Building DesignThe cross section of a precast concrete beam for a building is bounded by the graphs of the equations x = 2 1 + y 2 , x = − 2 1 + y 2 , y = 0 , and y = 3 where x and y are measured in feet. The length of the beam is 20 feet (see figure). (a) Find the volume V and the weight W of the beam. Assume the concrete weighs 148 pounds per cubic foot. (b) Find the centroid of a cross section of the beam.

Q: Expert Answer

(a) To determine To calculate: The cross section of the precast concrete beam of the building that is bounded by these equations, x = 2 1 + y 2 , x = − 2 1 + y 2 , y = 0 and y = 3 . Explanation Given: The equations for the beams are: x = 2 1 + y 2 , x = − 2 1 + y 2 , y = 0 and y = 3 . The length of the beam is 20 feet . Formula used: Volume of the beam: V = 2 ∫ 0 3 l x d y And ∫ 1 1 + x 2 = ln [ y + 1 + y 2 ] Calculation: Since, the length of the beam is 20 feet and the equations of the beam are: x = 2 1 + y 2 , x = − 2 1 + y 2 , y = 0 and y = 3 . Now, find the volume of the beam (b) To determine The centroid of the cross section of the concrete beam.

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Answer 1

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Calculus: Early Transcendental Fun...

6th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781285774770

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Answer 2

BuyFind

Calculus: Early Transcendental Fun...

6th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781285774770

Solutions

Chapter

Section

Answer 3

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Section

Answer 4

Chapter

Section

Answer 5

(a)

To determine

To calculate: The cross section of the precast concrete beam of the building that is bounded by these equations,x=21+y2,x=−21+y2,y=0 and y=3.

Explanation of Solution

Given: The equations for the beams are:

x=21+y2,x=−21+y2,y=0 and y=3.

The length of the beam is 20 feet.

Formula used:

Volume of the beam:

V=2∫03lxdy

And

∫11+x2=ln[y+1+y2]

Calculation:

Since, the length of the beam is 20 feet and the equations of the beam are:

x=21+y2,x=−21+y2,y=0 and y=3.

Now, find the volume of the beam

Answer 6

(b)

To determine

The centroid of the cross section of the concrete beam.

Calculus: Early Transcendental Fun...

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Calculus: Early Transcendental Fun...

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