A railroad tie (or sleeper) is subjected to two rail loads, each of magnitude P = 177 kN, acting as shown in the figure. a L 9 -a- The reaction q of the ballast is assumed to be uniformly distributed over the length of the tie, which has cross-sectional dimensions b = 300 mm and h = 250 mm. Calculate the maximum bending stress max (in MPa) in the tie due to the loads P, assuming the distance L = 1,500 mm and the overhang length a = 495 mm. (Enter the magnitude.) MPa
A railroad tie (or sleeper) is subjected to two rail loads, each of magnitude P = 177 kN, acting as shown in the figure. a L 9 -a- The reaction q of the ballast is assumed to be uniformly distributed over the length of the tie, which has cross-sectional dimensions b = 300 mm and h = 250 mm. Calculate the maximum bending stress max (in MPa) in the tie due to the loads P, assuming the distance L = 1,500 mm and the overhang length a = 495 mm. (Enter the magnitude.) MPa
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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![### Problem Description:
A railroad tie (or sleeper) is subjected to two rail loads, each of magnitude \( P = 177 \, \text{kN} \), acting as shown in the figure.
**Diagram Explanation:**
The diagram consists of a horizontal beam (representing the railroad tie) with two downward forces \( P \) at equal distances \( a \) from the edges. Beneath the beam, arrows pointing upward represent the uniformly distributed reaction \( q \) of the ballast.
The cross-section of the beam is shown as a rectangle with width \( b \) and height \( h \).
### Given Data:
- **Load, \( P \):** 177 kN
- **Cross-sectional Width, \( b \):** 300 mm
- **Cross-sectional Height, \( h \):** 250 mm
- **Distance Between Loads, \( L \):** 1500 mm
- **Overhang Length, \( a \):** 495 mm
- **Uniformly Distributed Reaction, \( q \):** Assumed to be uniformly distributed over the length of the tie.
### Problem Objective:
Calculate the maximum bending stress \( \sigma_{\text{max}} \) (in MPa) in the tie due to the loads \( P \).
### Solution:
Enter the calculated maximum bending stress \( \sigma_{\text{max}} \) based on the provided parameters.
\[ \sigma_{\text{max}} = \, \text{______ MPa} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7e73dffa-f7e2-4ec8-9d84-4f1c73b1a496%2Fe46e3469-6251-4a22-a4ab-8ccdc4ec9092%2F2vym4t6_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Description:
A railroad tie (or sleeper) is subjected to two rail loads, each of magnitude \( P = 177 \, \text{kN} \), acting as shown in the figure.
**Diagram Explanation:**
The diagram consists of a horizontal beam (representing the railroad tie) with two downward forces \( P \) at equal distances \( a \) from the edges. Beneath the beam, arrows pointing upward represent the uniformly distributed reaction \( q \) of the ballast.
The cross-section of the beam is shown as a rectangle with width \( b \) and height \( h \).
### Given Data:
- **Load, \( P \):** 177 kN
- **Cross-sectional Width, \( b \):** 300 mm
- **Cross-sectional Height, \( h \):** 250 mm
- **Distance Between Loads, \( L \):** 1500 mm
- **Overhang Length, \( a \):** 495 mm
- **Uniformly Distributed Reaction, \( q \):** Assumed to be uniformly distributed over the length of the tie.
### Problem Objective:
Calculate the maximum bending stress \( \sigma_{\text{max}} \) (in MPa) in the tie due to the loads \( P \).
### Solution:
Enter the calculated maximum bending stress \( \sigma_{\text{max}} \) based on the provided parameters.
\[ \sigma_{\text{max}} = \, \text{______ MPa} \]
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