### Educational Content: Analysis of Shearing Stress in Steel Shafts#### Problem Description:Two solid steel shafts, with a shear modulus \( G = 77.2 \, \text{GPa} \), are connected to a coupling disk \( B \) and to fixed supports at \( A \) and \( C \). For the loading shown in the diagram, the objectives are to determine:1. The reaction at each support.2. The maximum shearing stress in shaft \( AB \).3. The maximum shearing stress in shaft \( BC \).#### Diagram Explanation:- The system includes two shafts, \( AB \) and \( BC \).- The shaft \( AB \) extends 200 mm from the fixed support \( A \) to the coupling disk \( B \) where it has a diameter of 50 mm.- The shaft \( BC \) extends 250 mm from the coupling disk \( B \) to the fixed support \( C \) with a diameter of 38 mm.- A torque of \( 1.4 \, \text{kN} \cdot \text{m} \) is applied at the disk \( B \).This system is designed to study how torque affects the stress distribution in linked rotational components. The disk and shafts are designed to transmit rotational motion while withstanding the applied shear forces due to torque.#### Analytical Approach:- **Supports and Reactions:** Analyze the mechanical equilibrium to find forces at supports \( A \) and \( C \). - **Shearing Stress Calculation:** - Use the relation for maximum shearing stress, \( \tau_{\text{max}} = \frac{Tc}{J} \), where \( T \) is the torque, \( c \) is the outer radius, and \( J \) is the polar moment of inertia, \( J = \frac{\pi d^4}{32} \) for circular shafts. - **Equilibrium in Shafts:** Ensure that the imposed torque and the torsional reactions balance out, maintaining static equilibrium.This problem demonstrates practical applications of mechanics of materials, specifically involving torsion and stress analysis critical for designing shafts in mechanical systems.

Answered: Image /qna-images/answer/ba6234b9-73e5-4ab0-b0d2-1e3b9abd75c4.jpg

Two solid steel shafts (G = 77.2 GPa) are connected to a coupling disk B and to fixed supports at A and C. For the loading shown, determine (a) the reaction at each support, (b) the maximum shearing stress in shaft AB, (c) the maximum shearing stress in shaft BC. 200 mm 50 mm 250 mm 38 mm 1.4 kN - m

Two solid steel shafts (G = 77.2 GPa) are connected to a coupling disk B and to fixed supports at A and C. For the loading shown, determine (a) the reaction at each support, (b) the maximum shearing stress in shaft AB, (c) the maximum shearing stress in shaft BC. 200 mm 50 mm 250 mm 38 mm 1.4 kN - m

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: Question 1 B 900 mm 80 mm -40 mm T A The magnesium tube is bonded to the steel rod. Part A If the…

A: Shear stress of magnesium = 45 MPaShear stress of steel = 75 MPaModulus of rigidity magnesium = 18 ×…

Q: If the allowable shear strength of aluminum is 45 MPa, determine the minimum thickness, t, of the…

Q: solid steel shaft is made of steel has 100-mm diameter. The shaft is subjected to the distributed…

Q: Using Tall = 8.7 ksi and knowing that G= 5.6 x 106 psi, determine for each of the cold-rolled yellow…

Q: E' 3. For the 3-in.-diameter solid cylinder and loading shown, T = 40 kip-in., determine: (a) the…

Q: Given: 2 solid shafts of different materials are rigidly fastened together and supported as shown.…

Q: hollow brass (6000 ksi) shaft CD and a thin-walled steel (G=12000 ksi) tube DE. The whole assembly…

A: Find out:Maximum shear stress in the bolts at C (ksi)Maximum shear stress in the bolts at D (ksi)The…

Q: The solid rod AB has a diameter dAB5 60 mm and is made of a steel for which the allowable shearing…

A: Given Data: The diameter of the rod AB is: dAB= 60 mm The outer diameter of the pipe CD is: dCD=90…

Q: Q2) The aluminum rod BC (G-26 GPa) is bonded to the brass rod AB (G-39 GPa). Knowing that Birass…

A: For solution refer below images.

Q: Knowing thát the internal diameter of the HolUW SIlat shown is d= 23 mm, determine the maximum shear…

Q: The solid shaft shown is formed of a brass for which the allowable shearing stress is 55 MPa.…

A: if you have any doubts please comment

Q: The solid shaft (loaded as shown) is made of material that has an allowable shear stress of 10 MPa.…

A: The solid shaft (loaded as shown) is made of material that has an allowable shear stress of 10 MPa =…

Q: 3) The electric motor exerts a torque of 600 N.m on the steel shaft ABCD when it is rotating at a…

A: Given Data Modulus of rigidity is : G=77 GPa Length section of BC is : LBC=0.8 m Length section of…

Q: 16 kN 125 mm 3. The two boards are joined by plywood splices that are fully glued on the surfaces in…

Q: PROBLEM 3.52 A 4 kNm torque T is applied at end A of the composite shaft shown. Knowing that the…

Q: 2- The design of the gear-and-shaft system shown requires that steel shafts of the same diameter be…

A: or 0.0262 radG = 77 GPa

Q: angle of twist (a) between A and B, (b) between B and C, um (c) At C

Q: d₁ = 38 mm d₂

Q: 5. The torques shown are exerted on pulleys A and B. The diameter of the shaft AB is dAB = 50mm…

A: To transmit energy by rotation it is necessary to apply a turning force. in the case of a shaft if…

Q: The two shaft

A: Design of shaft is important process in any mechanical system. Design of shaft is determined by…

Q: 7o solid steel shafts are connected to f a disk B. Knowing the modulus of = d the allowable shear…

A: given:shear stress τ=90MPa

Q: The torque T causes a rotation of 2° at end B of the stainless-steel bar shown. Knowing that b = 20…

A: The rotation of the bar is .The distances are given as-The length of the bar is .The shear modulus…

Q: 3. The stepped shaft shown is supported by bearings at A and B. Determine the maximum stress in the…

A: Given Data r=3 mm

Q: 3.36 The torques shown are exerted on pulleys B. C, and D. Knowing that the entire shaft is made of…

A: To find the angle of twist

Concept explainers

Power Transmission Elements

It is defined as the energy transfer from one location to another location. The energy will start moving from the energy generation source to the energy applied position to obtain the work output. From this method, a large amount of electric energy moves from the power station to various electrical substations.

Question

### Educational Content: Analysis of Shearing Stress in Steel Shafts

#### Problem Description:

Two solid steel shafts, with a shear modulus \( G = 77.2 \, \text{GPa} \), are connected to a coupling disk \( B \) and to fixed supports at \( A \) and \( C \). For the loading shown in the diagram, the objectives are to determine:

1. The reaction at each support.
2. The maximum shearing stress in shaft \( AB \).
3. The maximum shearing stress in shaft \( BC \).

#### Diagram Explanation:

- The system includes two shafts, \( AB \) and \( BC \).
- The shaft \( AB \) extends 200 mm from the fixed support \( A \) to the coupling disk \( B \) where it has a diameter of 50 mm.
- The shaft \( BC \) extends 250 mm from the coupling disk \( B \) to the fixed support \( C \) with a diameter of 38 mm.
- A torque of \( 1.4 \, \text{kN} \cdot \text{m} \) is applied at the disk \( B \).

This system is designed to study how torque affects the stress distribution in linked rotational components. The disk and shafts are designed to transmit rotational motion while withstanding the applied shear forces due to torque.

#### Analytical Approach:

- **Supports and Reactions:** Analyze the mechanical equilibrium to find forces at supports \( A \) and \( C \).

- **Shearing Stress Calculation:**
- Use the relation for maximum shearing stress, \( \tau_{\text{max}} = \frac{Tc}{J} \),
where \( T \) is the torque, \( c \) is the outer radius, and \( J \) is the polar moment of inertia, \( J = \frac{\pi d^4}{32} \) for circular shafts.

- **Equilibrium in Shafts:** Ensure that the imposed torque and the torsional reactions balance out, maintaining static equilibrium.

This problem demonstrates practical applications of mechanics of materials, specifically involving torsion and stress analysis critical for designing shafts in mechanical systems.

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

Step 2

Sub part a

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 7 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Design of Power Transmission Elements and Power Transmission Systems

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

1. The member BD is attached to a rod at B, to a hydraulic cylinder at C, and to a fixed support at D. The bolt used at D acts in double shear and is made from a steel for which the maximum allowable shearing stress is Tallow = 40 ksi. The rod AB is made of a steel for which the maximum allowable tensile stress is Oallow = 60 ksi. The upward hydraulic force applied at C is 12 kip. 1) Calculate the minimum diameter of the rod AB. 2) Calculate the minimum diameter of the bolt at D. B FAB 12 kip 8 in. FBD
! Required information The torques shown are exerted on pulleys A, B, and C, where T₁ = 3 kip-in. and 72 = 7.4 kip-in. Assume that both shafts are solid and the diameter of shafts AB and BC to be 1.3 in. and 1.8 in., respectively. T1 10.4 kip.in. 48 in. B 72 in. T2 C Determine the maximum shearing stress in shaft AB. The maximum shearing stress in shaft AB is ksi.
The design specifications for the steel shaft AB require that the shaft acquire a strainenergy of 34 N.m as the 2.8 kN.m torque is applied. Using G = 72 GPa, determine(i) the largest inside diameter of the shaft that can be used,(ii) the corresponding maximum shearing stress in the shaft.
Required information The design of a machine element calls for a 40-mm-outer-diameter shaft to transmit 43 kW. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. 40 mm (a) (b) If the speed of rotation is 720 rpm, determine the maximum shearing stress in shaft a. The maximum shearing stress in shaft a is MPa.
Pravinbhai
UNIVERSITY of Prince Edward ISLAND i mm GGGG 54 mm T₁-1.2 kN-m 1-08 kNm 0 154 T-0.1 kN m 40 mm ASSIGNMENT 2.6 Under normal operating conditions, the electric motor exerts a torque of 2.4 kN m on shaft AB. Knowing that each shaft is solid, determine the maximum shearing stress in (a) shaft AB, (b) shaft BC, (c) shaft CD. ASSIGNMENT 2.7 Two shafts, each of -in. diameter, are connected by the gears shown. Knowing that G=11.2 x 10 psi and that the shaft at F is fixed, determine the angle through which end
The aluminum rod AB (G= 27 GPa) is bonded to the brass rod BD(G= 39 GPa). Knowing that portion CD of the brass rod is hollow and has an inner diameter of 40 mm, determine the angle of twist at A.
A 0.75" diameter solid steel shaft is connected by the steel bolted coupling shown. The maximum allowable shear stress in the steel is 18 ksi (shaft and bolts). The coupling consists of steel bolts that are 1/8" diameter and the bolt holes are equally spaced and centered on a 4" diameter circle (2" radius from the center of the shaft to the center of a bolt hole). Determine a) The maximum torque that the shaft can carry Ans: /,491"* b) The number of bolts required for the torque in part a). Assume the bolts fail by shearing at the coupling interface and the shear stress is uniform across the bolt's cross sectional area.
A stepped shaft ACB having solid circular cross sections with two different diameters is held against rotation at the ends (see figure Q2a). If the allowable shear stress in the shaft is 43 MPa, i) what is the maximum torque (To)max that may be applied at section C? ii) what is the angle of twist at point C (G=77.2 GPa) 20 mm 25 mm B То -225 mm- 450 mm Figure Q2a