**Title: Determining the Minimum Diameter for a Shaft under Load**---**Overview**This educational exercise involves determining the smallest diameter \( d \) of a shaft subjected to a bending stress. Given the conditions, the allowable bending stress is \(\sigma_{\text{allow}} = 130 \, \text{MPa}\).**Problem Statement**- **Supports:** The rod is supported by smooth journal bearings at points \( A \) and \( B \). These supports only exert vertical reactions on the shaft. - **Distributed Load:** The shaft is subjected to a uniform distributed load of \( 12 \, \text{kN/m} \).**Diagram Explanation**The diagram depicts a beam that is pinned at point \( A \) and supported by a roller at point \( B \):- **Length and Loading:** - The total span of the beam is \( 4.5 \, \text{m} \) (with sections of \( 3 \, \text{m} \) and \( 1.5 \, \text{m} \)). - The distributed load covers a portion of the span, creating a triangular loading pattern that peaks at \( 12 \, \text{kN/m} \).**Objective**Calculate the minimum diameter \( d \) of the shaft that can safely accommodate the given bending stress without failure.**Solution Approach**1. **Determine Reaction Forces:** Calculate the reactions at the supports using static equilibrium equations.2. **Draw Shear and Moment Diagrams:** Use the reactions to plot shear force and bending moment distributions along the beam.3. **Calculate Maximum Bending Moment:** Identify the location of the maximum bending moment.4. **Apply Bending Stress Formula:** Use the relationship \(\sigma = \frac{M \cdot c}{I}\) where: - \(\sigma\) is the bending stress, - \(M\) is the maximum bending moment, - \(c\) is the distance from the neutral axis to the outer fiber, - \(I\) is the moment of inertia.5. **Determine Minimum Diameter:** Rearrange and solve the equation for \( d \) given \(\sigma_{\text{allow}} = 130 \, \text{MPa}\).---**Interactive Section**- **Calculation Input:** A field for entering the calculated diameter \( d \) with the correct unit of measurement.**

Given data as per question Allowable stress =130 Mpa Distance between point A and B =3 m UDL applied…

Answered: Determine its smallest diameter d if…

Determine its smallest diameter d if the allowable bending stress is oallow = 130 MPa (Figure 1) Express vour answer with the appropriate units.

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

See similar textbooks

Related questions

Q: Which moment(s) will produce bending stress at H? Select all that apply. y My HK Mx M Mx My Mz x

A: Only M_x will produce a compressive Bending stress at HExplanation:M_x will produce a Compressive…

Q: 2. Given the box beam shown below, and concentrated load P=3500#. a. What is the magnitude of the…

Q: A simply supported beam is shown. The maximum bending moment is at B. Use the method of sections to…

A: Given Data: The allowable bending stress for the beam is, σb=24 ksi=24 ksi×144000 lb/ft2ksi=3456000…

Q: Find the absolute maximum bending stress in the beam shown in the figure below. (Figure 3) The beam…

Q: A simply supported beam supports the loads shown in the figure. The cross-sectional dimensions of…

Q: Applying the flexure formula, how can we determine the position of the absolute maximum bending…

A: The flexure formula is used to calculate the normal stress in the beam due to bending moment applied…

Q: Find the shear force and bending moment at point C. 4 kip/ft Answer: Vc = 4.8 kip (down) Mc = 19.2…

Q: | A Wa a ! B w. b C x

A: 1) Given : a= 7 ft , b=8.7 ft , wa=13 kipsft , wb=7kipsft Concept used : The conditions of…

Q: The compound beam is subjected to a unitorm dead load of 220 Ib/ft and a uniform ive load of 165…

Q: There is no F1 or F2 force, only P against the front end of the beam. Thank you so much for any help…

A: Given data-P=5KN=5000Nσy=240 mPa=240 ×106 N/m2

Q: Question 16 Calculate the maximum stress in the diagram below, con 0.06-in radius 2.00-in dia.…

A: GIVEN :- M=2800lb-inD=2 ind= 1.25 in SOLUTION :- finding stress concentration factor, taking D/d…

Q: Calculate the maximum internal bending moment in the shaft. Data: shaft diameter d3 50 mm; L=0.2 m;…

Q: For the surface area shown below, determine the second moment of area, the location of the neutral…

Q: Find the maximum shear stress. Assume that c1 = 8.273 in, c2 = 3.723 in, and I =

A: From the given shear force diagram of the loaded overhang beam, maximum shear force occurs at roller…

Q: A.) Determine maximum bending stress in the brass and steel. B.) Determine the stress at the seam…

A: M = 7.5 kN = 7500 NEbrass = 100 GPaEsteel = 200 GPa

Question

**Title: Determining the Minimum Diameter for a Shaft under Load**

---

**Overview**

This educational exercise involves determining the smallest diameter \( d \) of a shaft subjected to a bending stress. Given the conditions, the allowable bending stress is \(\sigma_{\text{allow}} = 130 \, \text{MPa}\).

**Problem Statement**

- **Supports:** The rod is supported by smooth journal bearings at points \( A \) and \( B \). These supports only exert vertical reactions on the shaft.

- **Distributed Load:** The shaft is subjected to a uniform distributed load of \( 12 \, \text{kN/m} \).

**Diagram Explanation**

The diagram depicts a beam that is pinned at point \( A \) and supported by a roller at point \( B \):

- **Length and Loading:**
- The total span of the beam is \( 4.5 \, \text{m} \) (with sections of \( 3 \, \text{m} \) and \( 1.5 \, \text{m} \)).
- The distributed load covers a portion of the span, creating a triangular loading pattern that peaks at \( 12 \, \text{kN/m} \).

**Objective**

Calculate the minimum diameter \( d \) of the shaft that can safely accommodate the given bending stress without failure.

**Solution Approach**

1. **Determine Reaction Forces:** Calculate the reactions at the supports using static equilibrium equations.
2. **Draw Shear and Moment Diagrams:** Use the reactions to plot shear force and bending moment distributions along the beam.
3. **Calculate Maximum Bending Moment:** Identify the location of the maximum bending moment.
4. **Apply Bending Stress Formula:** Use the relationship \(\sigma = \frac{M \cdot c}{I}\) where:
- \(\sigma\) is the bending stress,
- \(M\) is the maximum bending moment,
- \(c\) is the distance from the neutral axis to the outer fiber,
- \(I\) is the moment of inertia.
5. **Determine Minimum Diameter:** Rearrange and solve the equation for \( d \) given \(\sigma_{\text{allow}} = 130 \, \text{MPa}\).

---

**Interactive Section**

- **Calculation Input:** A field for entering the calculated diameter \( d \) with the correct unit of measurement.

**

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

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.

Similar questions

Find the max shear stress in a W12x50 cross-section using the appropriate estimated shear stress equation. Assume Vmax = 236kips.
The beam is subjected to an internal moment of M = 122 kN.m (Figure 1) Figure 30 mm, C. B 150 mm. M 150 mm 300 mm. 2 4 30 mm 1 of 1 ▼ Part A Determine the bending stress developed at point A. Express your answer to three significant figures and include the appropriate units. Enter negative value in the case of compression and positive value in the case of tension. A=148 Submit Part B μÁ MPa www Previous Answers Request Answer R= 624 MPa X Incorrect; Try Again; 4 attempts remaining ? Determine the bending stress developed at point B. Express your answer to three significant figures and include the appropriate units. Enter negative value in the case of compression and positive value in the case of tension.
The beam in (Figure 1) is made from three boards nailed together as shown. Figure d 20 mm 25 mm ✓ 200 mm M 150 mm 2 20 mm 1 of 1 Part A If the moment acting on the cross section is M = 460 Nm, determine the resultant force the bending stress produces on the top board. Express your answer to three significant figures and include appropriate units. F = Value Submit μA Provide Feedback 3 Request Answer Units ?
The shaft is subjected to the concentrated forces as shown in the figure below. There is a journal bearing at A and a thrust bearing at B. The allowable bending stress is σallow = 210 MPa. Determine, to the nearest mm, the smallest allowable diameter of the shaft.