The beam is subjected to a load F= 400 N and is supported by the rope and the smooth surfaces at A and B. Draw the free-body diagram of the beam. What are the magnitudes of the reactions at A and B?
The beam is subjected to a load F= 400 N and is supported by the rope and the smooth surfaces at A and B. Draw the free-body diagram of the beam. What are the magnitudes of the reactions at A and B?
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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The beam is subjected to a load F= 400 N and is supported by the rope and the smooth surfaces at A and B.
- Draw the free-body diagram of the beam.
- What are the magnitudes of the reactions at A and B?
Transcribed Image Text:This educational diagram illustrates a beam subject to various forces and angles. The main features of the diagram include:
- A horizontal beam placed on supports at two points, labeled as A and B.
- The beam is acted upon by a downward force (F) applied vertically at the center.
- The left end of the beam (A) rests against an inclined surface forming a 45° angle with the horizontal.
- The right end of the beam (B) rests on another inclined surface forming a 30° angle with the horizontal.
- Each support point exhibits different distances from the force application point:
- The distance from point A to the center point, where force F is applied, is marked as 1.2 meters.
- The distance from the center point to point B is marked as 1.5 meters.
- An additional distance extending beyond point B on the right side is marked as 1 meter.
This diagram can be used to demonstrate concepts such as equilibrium conditions, force components, moments, and other principles in static mechanics.
Transcribed Image Text:**Understanding Angles in Geometry**
Consider the following diagram that shows the angles.
### Diagram Explanation
The image consists of three labeled diagrams to demonstrate different geometric concepts related to angles.
1. **First Diagram: Lines and Angles on a Straight Line**
The first part of the image shows a horizontal straight line segment extended at both ends with several labeled points:
- Line segment \(AB\) lies horizontally.
- From point \(A\), a line extends upwards and to the left (point \(C\)).
- From point \(B\), a line extends downward and to the left (point \(C\)).
- A vertical line segment extends upwards from point \(F\) which lies between \(A\) and \(D\) on the straight line.
- Similarly, from point \(D\), a line extends upwards and to the left (point \(F\)).
- From point \(E\), a line extends downward and to the left (point \(F\)).
Red arrows are used to indicate the angles around points \(A\), \(D\), and \(F\).
2. **Second Diagram: Isosceles Triangle with Right Angle**
The second part of the image presents a triangle \(ACB\) with the following characteristics:
- The triangle is isosceles with angles:
- A right angle (90°) at vertex \(A\),
- Two 45° angles at vertex \(B\) and \(C\).
- The red arrow indicates all the angles inside the triangle \(ACB\).
3. **Third Diagram: Triangle with Right and Divided Angles**
The third part of the image shows a triangle \(DEF\) with a vertical line indicating additional angles:
- A vertical right angle (90°) is indicated at vertex \(D\).
- The triangle has internal angles of 30° and 60° divided as:
- 30° at vertex \(F\)
- 60° at vertex \(E\)
- The red arrow points these angles out to demonstrate their relations within the triangle \(DEF\).
### Educational Context
This diagram helps to understand angles in various geometric figures including straight lines and triangles. The correct identification and summation of angles are crucial concepts in geometry. For example, the angles in a triangle always sum up to 180°, and angles along a straight line sum up to
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