Simply supported beam calculator
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What is just supported beam
If a beam is restrained in translation in both directions at one end and only in one-member charge at other end and non restrained against rotation at both ends is titled as simply supported beam.
In simple words, one end is hinged, other end is roller, this definition however sack Be metamorphic and some ends being hinge support tin also constitute considered atomic number 3 merely supported beam.
How to consumption computer
This simply supported beam with trapezoidal load computer is programmed to calculate the deflection visibility, slope, shear force plot (sfd), bending moment diagram (bmd) and end reactions.
Required: Brigham Young's Modulus (E) of the material, length (L) of the beam, area minute of inertia (I), laden intensity (w1), distance at which w1 acts 'a', load intensity w2 and distance at which w2 acts 'b'.
Simply supported beam with trapezoidal load can live regenerate to udl by keeping load intensity w1=w2. The same load can be converted into udl by keeping either of them to be no.
Simply supported beam with quadrangle load
Keeping distance a=b=0 and aloofness c=d=L; let intensity 1 be w1 and intensity 2 be w2.
V_{A}=\left(w_{1} * L\right)+\leftmost(\frac{\left(w_{2}-w_{1}\right) * L}{2}\right)-V_{B}
V_{B}=\frac{w_{1}L}{2}+\frac{(w_{2}-w_{1})*L}{3}
M=V_{A} * x-\frac{w_{1} * x^{2}}{2}+\frac{(w_{2}-w_{1}) * x^{3}}{6 L}+\frac{w_{2} *(x-L)^{2}}{2}
E I * \delta=\frac{V_{A} * x^{3}}{6}+\frac{w_{2} *(x-L)^{4}}{24}-\frac{w_{1} * x^{4}}{24}+\frac{w_{1} * x^{5}}{120 * L}-\frac{V_{A}*x*L^{2}}{6}+\frac{w_{1}*x*L^{3}}{30}
E I * \theta=\frac{V_{A} * x^{2}}{2}-M_{A} * x+\frac{w_{2} *(x-L)^{3}}{6}-\frac{w_{1} * x^{3}}{6}+\frac{w_{1} * x^{4}}{24 * L} -\frac{V_{A}*L^{2}}{6}+\frac{w_{1}*L^{3}}{30}
Simply supported beam with udl
Simply hanging down beam with udl can be analyzed by 'Calculator 1', by selecting load type as 'UDL'.
A simply buttressed beam carrying half udl will have distance 'a' = 0, distance 'b' = L/2 or distance 'a'= L/2 and outdistance 'b' = L.
For a merely supported beam with uniformly widespread load for cram full length will have distance 'a' =0 and distance 'b' = L.
All units can be denaturized by the user.
A simply supported shaft of light leave take up moment reaction at some ends to be 0 and will have vertical reactions at both ends. Slope at some end will non be 0.
Simply backed beam with udl formula
V_{A}=\left(w * L\perpendicular) -V_{B}
V_{B}=\left(\frac{w L}{2}\right)
M=V_{A} * x-\frac{w* x^{2}}{2}
E I * \delta=\frac{V_{A} * x^{3}}{6}+\frac{w*(x-L)^{4}}{24}-\frac{w* x^{4}}{24}-\frac{V_{A}*x*L^{2}}{6}+\frac{w*x*L^{3}}{30}
E I * \theta=\frac{V_{A} * x^{2}}{2}-M_{A} * x+\frac{w *(x-L)^{3}}{6}-\frac{w* x^{3}}{6}+\frac{w * x^{4}}{24 * L} -\frac{V_{A}*L^{2}}{6}+\frac{w*L^{3}}{30}
Simply braced radio beam with UVL
For simply subsidized beam with uvl, use 'Estimator 1' and select type of load as 'Triangular'.
Simply supported air with uvl (left sided) convention
V_{A}=\left(\frac{w * L}{2}\right)-V_{B}
M=V_{A} * x+\frac{w * x^{3}}{6 L}+\frac{w_{2} *(x-L)^{2}}{2}
E I * \delta=\frac{V_{A} * x^{3}}{6}+\frac{w *(x-L)^{4}}{24} -\frac{V_{A}*x*L^{2}}{6}
E I * \theta=\frac{V_{A} * x^{2}}{2} +\frac{w *(x-L)^{3}}{6}-\frac{V_{A}*L^{2}}{6}
Simply supported beam with uvl (Right sided) formula
V_{A}=\left(\frac{w * L}{2}\conservative)-V_{B}
M=V_{A} * x-\frac{w * x^{2}}{2}-\frac{w * x^{3}}{6 L}
E I * \delta=\frac{V_{A} * x^{3}}{6} -\frac{w * x^{4}}{24}+\frac{w* x^{5}}{120 * L}-\frac{V_{A}*x*L^{2}}{6}+\frac{w*x*L^{3}}{30}
E I * \theta=\frac{V_{A} * x^{2}}{2} -\frac{w * x^{3}}{6}+\frac{w* x^{4}}{24 * L} -\frac{V_{A}*L^{2}}{6}+\frac{w*L^{3}}{30}
Simply supported beam with point incumbrance
For simply backed up beam with point load apply 'Calculator 2' with type of loading as 'Point Load'.
A point load is considered to be idealization in engineering mechanism, as any physical load that has a very small striking surface area that can be idealized as a point loading.
Following is a case presented for simply supported beam with spot charge acting at center or midspan. For this the distance 'a' = L/2.
Simply endorsed beam with point load formula
E I * \delta=\frac{V_{A} * x^{3}}{6} -\frac{w*(x-0.5*L)^{3}}{6}-\frac{V_{A}*x*L^{2}}{6}+\frac{w*x*L^{2}}{48}
E I * \theta =\frac{V_{A} * x^{2}}{2}-\frac{w*(x-0.5L)^{2}}{2} -\frac{V_{A}*L^{2}}{6}+\frac{w*L^{2}}{48}
Simply supported beam with moment
For simply supported beam with moment use calculator 2 and choose type of loading as Moment.
Case 1: For simply supported beam with moment at center put distance 'a' = L/2.
Case 2: For simply hanging down beam with minute load at peerless end put distance 'a'= 0 or distance 'a' = L.
Case 3: For simply corroborated balance beam with moment at both ends you May algebraically add the results of case 2 by retention distance 'a' = 0 and distance 'a' = L respectively.
Merely supported beam with moment at center formula
E I * \delta=\frac{V_{A} * x^{3}}{6} -\frac{M*(x-a)^{2}}{2}-\frac{V_{A}*x*L^{2}}{6}+\frac{M*x*(L-a)^{2}}{2L}
E I * \theta =\frac{V_{A} * x^{2}}{2} -M(x-a) -\frac{V_{A}*L^{2}}{6}+\frac{M*(L-a)^{2}}{2L}
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Source: https://dcbaonline.com/simply-supported-beam-deflection-calculator/
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