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Loads imposed on structures are supported by means of forces transmitted through structural elements. These forces can manifest themselves as tension (axial force), compression (axial force), shear, and bending, or flexure (a bending moment is a force multiplied by a distance, or lever arm, hence producing a turning effect or torque).
Another way to remember this is if the moment is bending the beam into a "smile" then the moment is positive, with compression at the top of the beam and tension on the bottom. [1] Normal positive shear force convention (left) and normal bending moment convention (right). This convention was selected to simplify the analysis of beams.
The vector T may be regarded as the sum of two components: the normal stress (compression or tension) perpendicular to the surface, and the shear stress that is parallel to the surface. If the normal unit vector n of the surface (pointing from Q towards P) is assumed fixed, the normal component can be expressed by a single number, the dot ...
In the absence of a qualifier, the term bending is ambiguous because bending can occur locally in all objects. Therefore, to make the usage of the term more precise, engineers refer to a specific object such as; the bending of rods, [2] the bending of beams, [1] the bending of plates, [3] the bending of shells [2] and so on.
A material being loaded in a) compression, b) tension, c) shear. Uniaxial stress is expressed by =, where F is the force acting on an area A. [3] The area can be the undeformed area or the deformed area, depending on whether engineering stress or true stress is of interest.
Chapter 3 – The Behavior of Bodies Under Stress Chapter 4 – Principles and Analytical Methods Chapter 5 – Numerical Methods Chapter 6 – Experimental Methods Chapter 7 – Tension, Compression, Shear, and Combined Stress Chapter 8 – Beams; Flexure of Straight Bars Chapter 9 – Bending of Curved Beams Chapter 10 – Torsion
σ(y) is the stress as a function of coordinate on the face of the beam. ρ is the radius of curvature of the beam at its neutral axis. θ is the bend angle. Since the bending is uniform and pure, there is therefore at a distance y from the neutral axis with the inherent property of having no strain:
We also assume that the sign convention of the stress resultants (and ) is such that positive bending moments compress the material at the bottom of the beam (lower coordinates) and positive shear forces rotate the beam in a counterclockwise direction.