What are some of the most used equations in civil engineering?

There are many important equations in Civil Engineering and it's vast area.But here i am mentioning some of them which are commonly in use eg.for load,shear, bending moment, deflection angle and deflection of simply supported beams which you may want to explore their applications on beams with different types of loading.
If w = the uniformly varying load on a beam:1.
W = SUM wdx.
Where W = the magnitude of the load at any point x from the reference support point.
(SUM means integral of)2.
V = SUM Wdx.
Where V = the shear at point x3.
M = SUM Vdx.
Where M = the bending moment at point x4.
EIA = SUM Mdx.
Where E = the modulus of elasticity of the beam material, I = the moment of inertia of the beam cross section, A = the deflection angle at the point x5.
EID = SUM Adx.
Where D = the deflection at the point.
With the above formulas, you can derive the equations for the maximum shear, bending moment and deflection of beams subjected to different types of loading and nature of support.
Not that if the load is uniformly distributed load, w =0 and the integral of Eq.1 reduces to W = C, where C = the value of the uniformly distributed load.
Also If the beam is loaded with a concentrated load V becomes a function of the reaction at the support.
Study these formulas and you will no longer have to be looking for references when you need to do shear, bending and deflection analysis.
If you consider another part of Civil Engineering:"Structural"portion,the mostly needed for bending is: M / I = f / y = E / R (or "may I find you ever ready").
Where M = bending moment, I = least second moment of inertia of the cross-section about an axis parallel to the axis of the applied loading, f = stress in outer fiber, at distance y from the neutral axis (of bending), E = Young's Modulus and R is the radius of curvature due to the applied load on the neutral axis.

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it depends on which area you are concentrating whether it will be on material take off, design, or costing.
But basically u need have a solid foundation on fractions (ratio and proportion), analytic and solid geometry formula, trigonometry and differential and integral calculus (because other formulas which you may forgot can be derived from calculus).

refer to the IS codes made for designing

stress=P/A P=load (Newton) A=Area of section in mm2