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A solid figure is the region of 3D space bounded by a two-dimensional closed surface; for example, a solid ball consists of a sphere and its interior. Solid geometry deals with the measurements of volumes of various solids, including pyramids, prisms (and other polyhedrons), cubes, cylinders, cones (and truncated cones). [2]
Constructive solid geometry (CSG; formerly called computational binary solid geometry) is a technique used in solid modeling. Constructive solid geometry allows a modeler to create a complex surface or object by using Boolean operators to combine simpler objects, [ 1 ] potentially generating visually complex objects by combining a few primitive ...
To a system of points, straight lines, and planes, it is impossible to add other elements in such a manner that the system thus generalized shall form a new geometry obeying all of the five groups of axioms. In other words, the elements of geometry form a system which is not susceptible of extension, if we regard the five groups of axioms as valid.
In solid mechanics and structural engineering, section modulus is a geometric property of a given cross-section used in the design of beams or flexural members.Other geometric properties used in design include: area for tension and shear, radius of gyration for compression, and second moment of area and polar second moment of area for stiffness.
Strength depends upon material properties. The strength of a material depends on its capacity to withstand axial stress, shear stress, bending, and torsion.The strength of a material is measured in force per unit area (newtons per square millimetre or N/mm², or the equivalent megapascals or MPa in the SI system and often pounds per square inch psi in the United States Customary Units system).
Concrete fracture analysis is part of fracture mechanics that studies crack propagation and related failure modes in concrete. [17] As it is widely used in construction, fracture analysis and modes of reinforcement are an important part of the study of concrete, and different concretes are characterized in part by their fracture properties. [ 18 ]
For slabs using spherical voids, the shear resistance is approximately proportional to the volume of concrete, as the geometry of the voids causes efficient transfer of force to load-bearing parts, enabling all the concrete to be effective. Other shapes of voids, with flat or flattened surfaces, will result in more concrete and/or less strength.
The determination of the stress and strain throughout a solid object is given by the field of strength of materials and for a structure by structural analysis. In the above figure, it can be seen that the compressive loading (indicated by the arrow) has caused deformation in the cylinder so that the original shape (dashed lines) has changed ...