load is applied to a beam as shown. Determine the equivalent force and location of the distributed load when a = 6 ft, b = ft, WA = 8 kips/ft and wg = 13 kips/ft WA A A a Parabola Vertex B WB

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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A distributed load is applied to a beam as shown. Determine the equivalent force and location of the distributed load when a = 6 ft, b = 7 ft, ωA = 8 kips/ft and ωB = 13 kips/ft.

**Diagram Explanation:**

- The diagram depicts a beam AB with a distributed load varying linearly across its length.
- The distributed load starts at point A with intensity \( \omega_A = 8 \) kips/ft and increases in a parabolic manner to \( \omega_B = 13 \) kips/ft at point B.
- The length from A to a certain point is marked as 'a' and from this point to B is denoted as 'b'. In this case, \( a = 6 \) ft and \( b = 7 \) ft.
- The load distribution forms a parabolic curve with its vertex along the beam.

**Calculation Requirements:**

The equivalent force is calculated as the area under the load distribution curve. Its location is determined using the centroid of the load shape.

_Fill in the blanks:_

The equivalent force is __ kips (Click to select) located __ ft left of point B.
Transcribed Image Text:A distributed load is applied to a beam as shown. Determine the equivalent force and location of the distributed load when a = 6 ft, b = 7 ft, ωA = 8 kips/ft and ωB = 13 kips/ft. **Diagram Explanation:** - The diagram depicts a beam AB with a distributed load varying linearly across its length. - The distributed load starts at point A with intensity \( \omega_A = 8 \) kips/ft and increases in a parabolic manner to \( \omega_B = 13 \) kips/ft at point B. - The length from A to a certain point is marked as 'a' and from this point to B is denoted as 'b'. In this case, \( a = 6 \) ft and \( b = 7 \) ft. - The load distribution forms a parabolic curve with its vertex along the beam. **Calculation Requirements:** The equivalent force is calculated as the area under the load distribution curve. Its location is determined using the centroid of the load shape. _Fill in the blanks:_ The equivalent force is __ kips (Click to select) located __ ft left of point B.
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