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MOW 217
What are Video Solutions?
Video Solutions are complete, step-by-step solution walkthroughs of representative homework problems from each section developed by Professor Ed Berger, University of Virginia.
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Chapter 5: Torsion
Chapter Objectives
In this chapter we will discuss the effects of applying a torsional loading to a long straight member such as a shaft or tube. Initially we will consider the member to have a circular cross section. We will show how to determine both the stress distribution within the member and the angle of twist when the material behaves in a linear–elastic manner and also when it is inelastic. Statically indeterminate analysis of shafts and tubes will also be discussed, along with special topics that include those members having noncircular cross sections. Lastly, stress concentrations and residual stress caused by torsional loadings will be given special consideration.
Shear Stress in Torsion [ SI ]
Allowable Torque [ SI ]
Static Indeterminacy in Torsion [ SI ]
Allowable Stress for Thin-Walled Tubes [ SI ]
Inelastic Torsion [ Non-SI ]
Interactive Animation
The animations help students visualize the relation between mathematical explanation and real structure, breaking down complicated sequences and showing how free-body diagrams can derived. These animations lend a graphic component to tutorials and lectures, assisting instructors in demonstrating the teaching concepts with greater ease and clarity.
Chapter 6: Bending
Chapter Objectives
Beams and shafts are important structural and mechanical elements in engineering. In this chapter we will determine the stress in these members caused by bending. The chapter begins with a discussion of how to establish the shear and moment diagrams for a beam or shaft. Like the normal-force and torque diagrams, the shear and moment diagrams provide a useful means for determining the largest shear and moment in a member, and they specify where these maximums occur. Once the internal moment at a section is determined, the bending stress can then be calculated. First we will consider members that are straight, have a symmetric cross section, and are made of homogeneous linear-elastic material. Afterward we will discuss special cases involving unsymmetric bending and members made of composite materials. Consideration will also be given to curved members, stress concentrations, inelastic bending, and residual stresses.
Chapter 6: Section 1, 2
Shear and Moment of a T-Beam [ Non-SI ]
Chapter 6: Section 4
Flexure Formula and Resultant Force [ Non-SI ]
Chapter 6: Section 5
Unsymmetric Bending [ SI ]
Chapter 6: Section 6
Sandwich Composite Beams [ Non-SI ]
Chapter 6: Section 7
Steel-Reinforced Composite Beams [ Non-SI ]
Chapter 6: Section 9
Stress Concentrations - Bending [ Non-SI ]
Elastic and Plastic Moment in Bending [ SI ]
Interactive Animation
The animations help students visualize the relation between mathematical explanation and real structure, breaking down complicated sequences and showing how free-body diagrams can derived. These animations lend a graphic component to tutorials and lectures, assisting instructors in demonstrating the teaching concepts with greater ease and clarity.
Chapter 7: Transverse Shear
Chapter Objectives
In this chapter, we will develop a method for finding the shear stress in a beam having a prismatic cross section and made from homogeneous material that behaves in a linear-elastic manner. The method of analysis to be developed will be somewhat limited to special cases of cross-sectional geometry. Although this is the case, it has many wide-range applications in engineering design and analysis. The concept of shear flow, along with shear stress, will be discussed for beams and thin-walled members. The chapter ends with a discussion of the shear center.
Transverse Shear and Shear Stress [ SI ]
Chapter 7: Section 1,2
Transverse Shear and Force Resultants [ Non-SI ]
Chapter 7: Section 3
Maximum Shear Stress in a Structure [ Non-SI ]
Chapter 7: Section 4
Shear Flow in a Nailed Structure [ Non-SI ]
Chapter 7: Section 4
Shear Flow in a Box Beam [ Non-SI ]
Shear Flow in a Thin Walled Structure [ SI ]
Chapter 8: Combined Loadings
Chapter Objectives
This chapter serves as a review of the stress analysis that has been developed in the previous chapters regarding axial load, torsion, bending, and shear. We will discuss the solution of problems where several of these internal loads occur simultaneously on a member’s cross section. Before doing this, however, the chapter begins with an analysis of stress developed in thin-walled pressure vessels.
Pressure Vessels and Thermal Strain [ Non-SI ]
Chapter 8: Section 2
Combined Loading - Multiple Forces [ Non-SI ]
Chapter 8: Section 2
Combined Loading - Hook Geometry [ Non-SI ]
Combined Loading - Curved Geometry [ SI ]
Chapter 9: Stress Transformation
Chapter Objectives
In this chapter, we will show how to transform the stress components that are associated with a particular coordinate system into components associated with a coordinate system having a different orientation. Once the necessary transformation equations are established, we will then be able to obtain the maximum normal and maximum shear stress at a point and find the orientation of elements upon which they act. Plane-stress transformation will be discussed in the first part of the chapter, since this condition is most common in engineering practice. At the end of the chapter we will discuss a method for finding the absolute maximum shear stress at a point when the material is subjected to both plane and three-dimensional states of stress.
Chapter 9: Section 1, 2
Stress Transformations - Transform Equations [ Non-SI ]
Chapter 9: Section 1, 2
Stress Transformations=Stress Summation [ SI ]
Chapter 9: Section 4
Principal Stresses and Max. In-Plane Shear [ SI ]
Chapter 9: Section 4
Principal Stresses in a Dam [ Non-SI ]
Chapter 9: Section 4
Principal Stresses - 3-D Loading [ Non-SI ]
Chapter 9: Section 7
Absolute Maximum Shear Stress [ SI ]
Interactive Animation
The animations help students visualize the relation between mathematical explanation and real structure, breaking down complicated sequences and showing how free-body diagrams can derived. These animations lend a graphic component to tutorials and lectures, assisting instructors in demonstrating the teaching concepts with greater ease and clarity.
Mohr’s Circles
Videos