homework-statics, engineering homework help

User Generated

NNNN94

Engineering

Description

homework

Unformatted Attachment Preview

QUESTION 1 Locate the centroid of the plane area shown if h = 15 in. Round the final answer to two decimal places. QUESTION 2 Locate the centroid of the plane area shown if l = 124 mm. Round the final answer to one decimal place. QUESTION 3 Locate the centroid of the plane area shown. QUESTION 4 Locate the centroid of the plane area shown. QUESTION 5 A uniform circular rod of weight 16 lb and radius 10 in. is attached to a pin at C and to the cable AB. Determine the tension in the cable. (Round the final answer to two decimal places.) (You must provide an answer before moving to the next part.) QUESTION 6 Determine by direct integration the centroid of the area shown. Express your answer in terms of a and h. QUESTION 7 Determine the reactions at the beam supports for the given loading if W = 200 lb/ft. Round the final answer to the nearest whole number QUESTION 8 A beam is subjected to a linearly distributed downward load and rests on two wide supports BC and DE, which exert uniformly distributed upward loads as shown. Determine the values of wBC and wDE corresponding to equilibrium when wA = 750 N/m. Round the final answer to the nearest whole number QUESTION 9 Determine the centroid of the area shown by direct integration. Express your answer in terms of a and h.
Purchase answer to see full attachment
User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.

Explanation & Answer

Hi, find attached your answers. In case you need any clarification, please let me know. I hope the work will meet your expectations.

QUESTION 1
Locate the centroid of the plane area shown if h = 15 in. Round the final answer to two decimal
places.

We find the area of the shaded area by first dividing it into two shapes; a triangle and a rectangle.

𝐴1 = 6 ∗ 3 = 18𝑖𝑛2
𝐴2 =
6

1
1
∗ ℎ ∗ 12 = ∗ 15 ∗ 12 = 90𝑖𝑛2
2
2

3

Centroid of 𝐴1 = (6 + 2 , ℎ + 2) = (9,16.5)
1
3

Centroid of a right angle triangle is at a distance of ∗ 𝑏 𝑎𝑛𝑑
1

Centroid of 𝐴2 along x-axis, 3 ∗ 12 = 4𝑖𝑛

1
3

∗ ℎ from the angle, therefore;

1

2

2

Along y-axis, ℎ − 3 ∗ ℎ = 3 ℎ = 3 ∗ 15 = 10𝑖𝑛
Centroid of 𝐴2 = (4,10)
To find the centroid of the shaded area, we use area moments. Moment at the centroid is zero.
Let 𝑥 and 𝑦 be the points of the centroid along x-axis and y-axis respectively.
Moments along y-axis,
(18 ∗ 9) + (90 ∗ 4) = 𝐴 ∗ 𝑥
Where 𝐴 is the total area, 𝐴1 + 𝐴2
162 + 360 = (90 + 18) ∗ 𝑥
Simplifying,
𝑥=

162 + 360 522
=
= 4.83𝑖𝑛
(90 + 18) 108

Moments along x-axis,
(18 ∗ 16.5) + (90 ...


Anonymous
Excellent! Definitely coming back for more study materials.

Studypool
4.7
Trustpilot
4.5
Sitejabber
4.4

Related Tags