(5) Given the below 40 ft beam with the distributed load of 2 kips/ft and a point load of 16 kips: (a) What are the reactions (forces) at supports A and B? (b) Draw the shear V and the bending moment M diagrams in the graphs below.

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
icon
Related questions
icon
Concept explainers
Question
5a and 5b
### Problem Statement:

Given the below 40 ft beam with the distributed load of 2 kips/ft and a point load of 16 kips:

(a) What are the reactions (forces) at supports A and B?  
(b) Draw the shear \( V \) and the bending moment \( M \) diagrams in the graphs below.  
(c) What is \( V_{\text{max}} \) and where in \( x \) is it located?  
(d) What is \( M_{\text{max}} \) and where in \( x \) is it located?

### Diagram Explanation:

**Beam Diagram:**

- A 40 ft beam is supported at two points: A (roller) and B (pin).  
- Distance between A and B is divided into four 10 ft sections.  
- A distributed load of 2 kips/ft spans between A and a point 10 ft away, and a concentrated point load of 16 kips is applied at the midpoint of the beam (20 ft from A).

**Graph Explanation:**

1. **Shear Force Diagram (V) Placeholder:**

   - X-axis denotes the position \( x \) along the beam.
   - Y-axis indicates the shear force \( V \).
   - Intervals on the x-axis correspond to the positions at every 10 ft along the beam.

2. **Bending Moment Diagram (M) Placeholder:**

   - Similarly, the x-axis represents the beam position \( x \).
   - The y-axis shows the bending moment \( M \).
   - The graph is structured to detail changes in moment values across the beam’s length.

### Notes for Educational Purpose:

- Analyze the beam using equilibrium equations to find reactions at A and B.
- Develop shear and moment equations for different segments of the beam based on loading conditions.
- Plot corresponding shear and moment values at key points.
- Use these plots to determine maxima for shear and bending moment, as requested in parts (c) and (d).
Transcribed Image Text:### Problem Statement: Given the below 40 ft beam with the distributed load of 2 kips/ft and a point load of 16 kips: (a) What are the reactions (forces) at supports A and B? (b) Draw the shear \( V \) and the bending moment \( M \) diagrams in the graphs below. (c) What is \( V_{\text{max}} \) and where in \( x \) is it located? (d) What is \( M_{\text{max}} \) and where in \( x \) is it located? ### Diagram Explanation: **Beam Diagram:** - A 40 ft beam is supported at two points: A (roller) and B (pin). - Distance between A and B is divided into four 10 ft sections. - A distributed load of 2 kips/ft spans between A and a point 10 ft away, and a concentrated point load of 16 kips is applied at the midpoint of the beam (20 ft from A). **Graph Explanation:** 1. **Shear Force Diagram (V) Placeholder:** - X-axis denotes the position \( x \) along the beam. - Y-axis indicates the shear force \( V \). - Intervals on the x-axis correspond to the positions at every 10 ft along the beam. 2. **Bending Moment Diagram (M) Placeholder:** - Similarly, the x-axis represents the beam position \( x \). - The y-axis shows the bending moment \( M \). - The graph is structured to detail changes in moment values across the beam’s length. ### Notes for Educational Purpose: - Analyze the beam using equilibrium equations to find reactions at A and B. - Develop shear and moment equations for different segments of the beam based on loading conditions. - Plot corresponding shear and moment values at key points. - Use these plots to determine maxima for shear and bending moment, as requested in parts (c) and (d).
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 4 images

Blurred answer
Knowledge Booster
Design Against Fluctuating Loads
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Elements Of Electromagnetics
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY