2.22 A simply supported beam is loaded as shown in Fig. P2.22. Using singularity func- tions, the displacement along the beam can be expressed by the equation -5 14,(x) = [(x − 0)ª − (x − 5)¹] + 15√(x − 8)³ 6 +75 (x-7)²+²-238.25x By definition, the singularity function can be expressed as follows: x = {"x = [(x-a)" whenx > a} 0 when x
2.22 A simply supported beam is loaded as shown in Fig. P2.22. Using singularity func- tions, the displacement along the beam can be expressed by the equation -5 14,(x) = [(x − 0)ª − (x − 5)¹] + 15√(x − 8)³ 6 +75 (x-7)²+²-238.25x By definition, the singularity function can be expressed as follows: x = {"x = [(x-a)" whenx > a} 0 when x
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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![### Educational Content on Beam Displacement
**Figure P2.22 Explanation**
A simply supported beam is loaded as depicted in the diagram. The loading conditions consist of:
- A distributed load of 20 kips/ft over a portion of the beam.
- A concentrated moment of 150 kip-ft applied to the beam, located beyond the midpoint.
- A distributed load of 15 kips/ft over the remaining portion of the beam.
**Equation for Displacement**
The displacement \( u(x) \) along the beam can be mathematically described using singularity functions:
\[
u(x) = -\frac{5}{6} \langle x - 0 \rangle^4 + \frac{15}{6} \langle x - 8 \rangle^3 + 75 \langle x - 7 \rangle^2 + \frac{57}{6} x^3 - 238.25x
\]
**Singularity Function Definition**
The singularity function is expressed as:
\[
\langle x - a \rangle^n =
\begin{cases}
(x - a)^n & \text{when } x > a \\
0 & \text{when } x \le a
\end{cases}
\]
**Programming Task**
Create a program to plot displacement versus distance \( x \) along the beam. The position \( x = 0 \) is at the left end of the beam.
**Diagram Description**
- The beam is shown with two distributed loads and a moment.
- The left supported reaction is shown at the start of the beam.
- Distributed loads and moments are clearly marked and dimensioned.
This setup is used to study the displacement of the beam under the given load conditions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd20dfe5a-a4c1-4793-9f05-a80ad59a67d4%2F4bf5c29d-7ca7-41c5-b833-31fae6900c04%2Fyolwx7_processed.png&w=3840&q=75)
Transcribed Image Text:### Educational Content on Beam Displacement
**Figure P2.22 Explanation**
A simply supported beam is loaded as depicted in the diagram. The loading conditions consist of:
- A distributed load of 20 kips/ft over a portion of the beam.
- A concentrated moment of 150 kip-ft applied to the beam, located beyond the midpoint.
- A distributed load of 15 kips/ft over the remaining portion of the beam.
**Equation for Displacement**
The displacement \( u(x) \) along the beam can be mathematically described using singularity functions:
\[
u(x) = -\frac{5}{6} \langle x - 0 \rangle^4 + \frac{15}{6} \langle x - 8 \rangle^3 + 75 \langle x - 7 \rangle^2 + \frac{57}{6} x^3 - 238.25x
\]
**Singularity Function Definition**
The singularity function is expressed as:
\[
\langle x - a \rangle^n =
\begin{cases}
(x - a)^n & \text{when } x > a \\
0 & \text{when } x \le a
\end{cases}
\]
**Programming Task**
Create a program to plot displacement versus distance \( x \) along the beam. The position \( x = 0 \) is at the left end of the beam.
**Diagram Description**
- The beam is shown with two distributed loads and a moment.
- The left supported reaction is shown at the start of the beam.
- Distributed loads and moments are clearly marked and dimensioned.
This setup is used to study the displacement of the beam under the given load conditions.
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