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Chapter 4: Problem 76

How can an engineer best explain why free-body diagrams are so important in determining forces and stresses?

Short Answer

Expert verified
Free-body diagrams are crucial in engineering as they provide a visual representation of the external forces acting on an object. This helps in understanding the physical interactions within the system and enables the engineer to use laws of physics, like Newton's laws, to calculate these forces and consequently determine the resulting stresses and deformations.

Step by step solution

01

Understanding the Concept

Hence, the first step is to understand the concept of free-body diagrams. It's a graphical illustration used by engineers to visualize physical interactions of different forces acting on a body. The body under consideration is isolated and all forces acting upon it are depicted.
02

Importance in Engineering

Next, one must comprehend the significance of these diagrams in the field of engineering. Since engineers often have to work with systems in equilibrium, these diagrams provide a clear visual understanding of the various forces that the structure or mechanism is subjected to. It illustrates every force acting on the object and indicates whether the object is static or dynamic.
03

Determining Forces and Stresses

This step is about how these diagrams aid in determining forces and stresses. By clearly outlining the forces acting on a system, engineers can then use Newton's laws of motion to calculate the values of these forces. After identifying the forces, they can apply mechanical theories to determine the stresses and deformations.

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Most popular questions from this chapter

A stainless steel member has a three-dimensional state of stress at a critical location where \(\sigma_{x}=50,000, \sigma_{y}=-10,000, \sigma_{z}=15,000 . \tau_{\mathrm{xy}}=-3500, \tau_{\mathrm{yz}}=-1000\), and \(\tau_{\mathrm{zx}}=\) 2000 psi. Calculate the first, second, and third stress invariants and solve the characteristic equation for the principal normal stresses. Also, calculate the maximum shear stress and draw the Mohr circle representation of the state of stress at the critical point.

A cylindrical ring has an outer diameter \(D\), an inner diameter \(d\), and a width \(w\). A solid cylindrical disk of diameter \((d+\Delta d)\) and width \(w\) is press fit completely into the ring. If the ring were thin (i.e., \((D-d)\) is very small), how could you calculate the pressure on the outer cylindrical surface of the inner cylinder disk?

The inner surface of a hollow cylinder internally pressurized to \(100 \mathrm{MPa}\) experiences tangential and axial stresses of 600 and \(200 \mathrm{MPa}\), respectively. Make a Mohr circle representation of the stresses in the inner surface. What maximum shear stress exists at the inner surface?

Determine the maximum shear stress at the outer surface of an internally pressurized cylinder where the internal pressure causes tangential and axial stresses in the outer surface of 300 and \(150 \mathrm{MPa}\), respectively.

A 30 -mm-diameter shaft transmits \(700 \mathrm{~kW}\) at \(1500 \mathrm{rpm}\). Bending and axial loads are negligible. (a) What is the nominal shear stress at the surface? (b) If a hollow shaft of inside diameter \(0.8\) times outside diameter is used, what outside diameter would be required to give the same outer surface stress? (c) How do weights of the solid and hollow shafts compare?
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