REQUIREMENT OF COMPATIBILITY CONDITIONS
A direct determination of the six stress components requires six equations—three equilibrium equations and three compatibility conditions. However, indirect methods can be obtained by transforming stress into displacement or scalar…
Classification of the Response of Materials
First, it should be clarified that one should not get confused with the real body and its mathematical idealization. Modeling is all about idealizations that lead to predictions that are…
Basic Equations in Mechanics
Having gained a superficial understanding of the four concepts in mechanics namely the force, stress, displacement and strain, let us look at the four equations that connect these concepts and…
Equilibrium and compatibility
Introduction This course builds upon the concepts learned in the course “Mechanics of Materials” also known as “Strength of Materials”. In the “Mechanics of Materials” course one would have learnt…
Vertical Retaining Wall Structures
Overview Vertical wall type structures function as barriers whose purpose is to prevent a material from entering a certain space. Typical applications are embankment walls, bridge abutments, and as underground…
Shallow Foundations
Overview In most cases civil structures are placed on the ground. That segment of the structure which interfaces with the ground is called the foundation. In this chapter, we focus…
Statically Determinate Curved Members
Overview Beams are straight members subjected to transverse loading. We showed there that transversely loaded beams respond by bending, i.e., they equilibrate the loading by developing internal shear and moment…
Cables Subjected to Concentrated Loads
Horizontal Cables Suppose we conduct the following experiment shown in Fig. 5.6. We start with a horizontally aligned cable that is pin connected at A, supported with a roller support…
Displacement and Deformation of Slender Beams: Planar Loading
Figure 3.18 shows how a slender beam responds to a transverse planar loading. The geometric quantities that define the movement of the beam from its unloaded position due to an…
Definition of a Prismatic Beam
Beams are used extensively in structures, primarily in flooring systems for buildings and bridges. They belong to the line element category, i.e. their longitudinal dimension is large in comparison to…
