In geometry, a locus (plural: loci) (Latin word for “place”, “location”) is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.

In mathematics, curvature is any of several strongly related concepts in geometry. Intuitively, the curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane. Smaller circles bend more sharply, and hence have higher curvature.

If a curve is given by the polar equation r=r(θ), the curvature is calculated by the formula. K=∣∣r2+2(r′)2−rr′′∣∣[r2+(r′)2]32. The radius of curvature of a curve at a point M(x,y) is called the inverse of the curvature K of the curve at this point: R=1K.

[′kər·və·chər i′fekt] (electronics) Generally, the condition in which the dielectric strength of a liquid or vacuum separating two electrodes is higher for electrodes of smaller radius of curvature.

Curvature Synonyms – WordHippo Thesaurus….What is another word for curvature?

arc	bend
curve	arching
curving	angle
arch	bow
crook	curvity

What is the opposite of curvature?

failure	inability
miss	stagnation

1 : the act of curving : the state of being curved. 2 : a measure or amount of curving specifically : the rate of change of the angle through which the tangent to a curve turns in moving along the curve and which for a circle is equal to the reciprocal of the radius.

1 : the quality or state of being flexed : flexion. 2 : turn, bend, fold.

As nouns the difference between bend and flexure is that bend is a curve while flexure is the act of bending or flexing; flexion.

Pure bending ( Theory of simple bending) is a condition of stress where a bending moment is applied to a beam without the simultaneous presence of axial, shear, or torsional forces. Pure bending occurs only under a constant bending moment (M) since the shear force (V), which is equal to. , has to be equal to zero.

Beam bending theory is often used in the somewhat more general context in which the bending moment varies along the beam. The theory of nonhomogeneous bending – or flexure – of a beam thereby corresponds to a particular location of the transverse force with respect to the beam cross-section.

Behaviour of reinforced masonry has been studied experimentally to determine its strength potential. The increase in either compressive or tensile strength of masonry is possible due to the existence of rebar or wire mesh.

Flexural strength is one measure of the tensile strength of concrete. It is a measure of an un-reinforced concrete beam or slab to resist failure in bending. Flexural MR is about 10 to 20 percent of compressive strength depending on the type, size and volume of coarse aggregate used.

Bending stress is a more specific type of normal stress. The stress at the horizontal plane of the neutral is zero. The bottom fibers of the beam undergo a normal tensile stress. It can be concluded therefore that the value of the bending stress will vary linearly with distance from the neutral axis.

The bending stress is computed for the rail by the equation Sb = Mc/I, where Sb is the bending stress in pounds per square inch, M is the maximum bending moment in pound-inches, I is the moment of inertia of the rail in (inches)4, and c is the distance in inches from the base of rail to its neutral axis.

When a beam is subjected to external loads, shear forces and bending moments develop in the beam. Therefore, a beam must resist these external shear forces and bending moments. The stresses caused by the bending moments are called bending stresses.

The maximum bending stress occurs at the top surface of the die, and its location is corresponding to the inner bumps of the bottom die. The deflection of the beam is proportional to the bending moment, which is also proportional to the bending force.

The bending stress increases linearly away from the neutral axis until the maximum values at the extreme fibers at the top and bottom of the beam. The maximum bending stress is given by: where c is the centroidal distance of the cross section (the distance from the centroid to the extreme fiber).

So to calculate the flexural strength (σ), multiply the force by the length of the sample, and then multiply this by three. Then multiply the depth of the sample by itself (i.e., square it), multiply the result by the width of the sample and then multiply this by two. Finally, divide the first result by the second.

midspan

For example, if a beam is loaded by a uniformly distributed load across the full length of the beam, the equation for maximum bending moment is M=wL^2/8, where w is the value of the load (per unit length) and L is the span of the beam.

Explanation: The bending moment at a section is considered to be positive when it causes convexity downwards such bending moment is called sagging bending moment positive bending moment.

A uniformly distributed load (UDL) is a load that is distributed or spread across the whole region of an element such as a beam or slab. In other words, the magnitude of the load remains uniform throughout the whole element.

The load may be represented as rate per lineal metre (kN/m) for beams, or as a rate per square metre (kN/m2) for slabs. A diagram shows a beam with the load distributed all along its length. The load is labelled UDL with units shown as kN/m or kN/m2.

For solving the problems, total UDL can be converted into a point load, acting at center of UDL. Uniformly Varying Load (UVL) A UVL is one which is spread over the beam in such a manner that rate of loading varies from each point along the beam, in which load is zero at one end and increase uniformly to the other end.

21 Types of Beams in Construction [PDF]

• Simply Supported Beam.
• Fixed Beam.
• Cantilever Beam.
• Continuous Beam.
• Reinforced Concrete Beams.
• Steel Beams.
• Timber beams.
• Composite Beams.

Multiply the load per unit area or length by the total area or length. For the rectangle, you compute 10 kN per square meter multiplied by 24 square meters to get 240 kN. For the beam, you calculate 10 kN per meter multiplied by 5 meters to get 50 kN.