<p>Simple Beam Function</p>

720156b7-d07e-414b-81ef-1da54af08546 8 4 5 decimal

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ST L E I w w.p Pt n.n fSB Define Stepwise Function x a n fsin x a - (n^x a > (* n 0 ≥ (* : Put loads into proper variable names n 1 Pt cols range P 1 n el Pt 1 n el : a 1 n el Pt 2 n el : 21 line for n 1 w.p cols range w.b 1 n el w.p 1 n el : w.e 1 n el w.p 3 n el : b 1 n el w.p 2 n el : e 1 n el w.p 4 n el : 41 line for Nothing to Clear in there Shear Loading Functions x F.VP P 1 m el x a 1 m el 0 fsin * - (m 1 P cols sum : x F.Vw w 1 m el x 0 ft * 1 fsin x L 1 fsin - (* - (m 1 w cols sum : x F.Vwp w.e 1 m el w.b 1 m el - 2 e 1 m el b 1 m el - (* / x b 1 m el 2 fsin x e 1 m el 2 fsin - (* - w.b 1 m el x b 1 m el 1 fsin * - w.e 1 m el x e 1 m el 1 fsin * + (m 1 w.p cols sum : x F.V x F.VP x F.Vw + x F.Vwp + : 41 line Moment Loading Functions x F.MP P 1 m el x a 1 m el 1 fsin * - (m 1 P cols sum : x F.Mw w 1 m el 2 / x 0 ft * 2 fsin x L 2 fsin - (* - (m 1 w cols sum : x F.Mwp 13! / w.e 1 m el w.b 1 m el - e 1 m el b 1 m el - / * x b 1 m el 3 fsin x e 1 m el 3 fsin - (* - 12 / w.b 1 m el x b 1 m el 2 fsin * w.e 1 m el x e 1 m el 2 fsin * - (* - (m 1 w.p cols sum : x F.M x F.MP x F.Mw + x F.Mwp + : 41 line Rotation Loading Functions x F.θP P 1 m el x a 1 m el 2 fsin * 2 E * I * / - (m 1 P cols sum : x F.θw w 1 m el 3! (E * I * / x 0 ft * 3 fsin x L 3 fsin - (* - (m 1 w cols sum : x F.θwp 14! (E * I * / w.e 1 m el w.b 1 m el - e 1 m el b 1 m el - / * x b 1 m el 4 fsin x e 1 m el 4 fsin - (* - 13! (E * I * / w.b 1 m el x b 1 m el 3 fsin * w.e 1 m el x e 1 m el 3 fsin * - (* - (m 1 w.p cols sum : x F.θ x F.θP x F.θw + x F.θwp + : 41 line Deflection Loading Function x F.yP P 1 m el x a 1 m el 3 fsin * 3! (E * I * / (m 1 P cols sum : x F.yw w 1 m el 4! (E * I * / x 0 ft * 4 fsin x L 4 fsin - (* (m 1 w cols sum : x F.ywp 15! (E * I * / w.e 1 m el w.b 1 m el - e 1 m el b 1 m el - / * x b 1 m el 5 fsin x e 1 m el 5 fsin - (* 14! (E * I * / w.b 1 m el x b 1 m el 4 fsin * w.e 1 m el x e 1 m el 4 fsin * - (* - (m 1 w.p cols sum : x F.y x F.yP x F.yw + x F.ywp + : 41 line Boundary Conditions ST Pin-Pin ≡ V.0 1 L / L F.M * - eval : M.0 0 kip * ft * eval : θ.0 1 L / L F.y * L 6 E * I * / L F.M * + eval : y.0 0 in * eval : 41 line Boundary Condition Not Programed if 11 line Equations for Bending of Euler-Bernoulli Beam x V V.0 x F.V + : x M M.0 V.0 x * + x F.M + : x θ θ.0 M.0 x E I * / * - V.0 x 2^2 E * I * / * - x F.θ + : x y y.0 θ.0 x * - M.0 x 2^2 E * I * / * - V.0 x 3^3! (E * I * / * - x F.y + : 41 line Find Max Shear, Moment and Deflection x f x1 GetMax fmax 0 : X.max# 0 ft * : i 1 n.n range x1 i el L i 1 - n.n 1 - / * : f i el x1 i el f : f i el abs fmax > fmax f i el abs : X.max# x1 i el : 21 line 0 if 31 line for fmax X.max# 21 sys 41 line : V.max X V x GetMax : M.max X M x GetMax : y.max X y x GetMax : 41 line V.max M.max y.max P 41 sys 211 line :

Nomenclature flows that found in "Beam Analysis spreadsheet" by Alex Tomanovich

Span Type

ST Pin-Pin :

Length

L 20 ft * :

MoE

E 29000 ksi * :

MoI

I 100 in 4^* :

w 0 kip ft / * 0 kip ft / * 12 mat :

Uniform Load

Partial Loads

w.p 0 kip ft / * 0 kip ft / * 0 kip ft / * 2 ft * 2 ft * 3 ft * 10 kip ft / * 0 kip ft / * 0 kip ft / * 8 ft * 10 ft * 6 ft * 43 mat :

Enter wb in top row

Enter b in second row

Load

Enter we in third row

Enter e in bottom row

Point Loads

Pt 0 kip * 0 kip * 5 ft * 4 ft * 22 mat :

Numnber of points to divide beam

n.n 50 :

Results ST L E I w w.p Pt n.n fSB :

V.max Results 11 el : kip 21

X.Vmax Results 21 el : ft 0

M.max Results : 31 el kip ft * 112.252

X.Mmax Results 41 el : ft 6.9388

y.max Results 51 el : in 5.0485

X.ymax Results 61 el : ft 15.5102