1b1673c1-dc58-4d22-9e18-53310bd0cad8 5 4 5 false false 0 decimal

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x f.1 a.1 x 3^* b.1 x 2^* + c.1 x * + d.1 + :

x f.2 a.2 x 3^* b.2 x 2^* + c.2 x * + d.2 + :

Eqn 0 f.1 0 ≡ a f.1 a f.2 ≡ L f.2 0 ≡ x f.1 x diff x a ≡ at x f.2 x diff x a ≡ at ≡ x f.1 x 2 diff x 0 ≡ at 0 ≡ x f.2 x 2 diff x L ≡ at 0 ≡ x f.1 x 2 diff x a ≡ at x f.2 x 2 diff x a ≡ at ≡ x f.1 x 3 diff x a ≡ at x f.2 x 3 diff x a ≡ at F E I * / - (≡ 81 sys :

vars a.1 a.2 b.1 b.2 c.1 c.2 d.1 d.2 81 sys :

Eqn vars Solve Assign F a L - (* 6 E * I * L * / F a * 6 E * I * L * / 0 F a * 2 E * I * / - F a * a a 3 L * - (* 2 L 2^* + (* 6 E * I * L * / F a * a 2^2 L 2^* + (* 6 E * I * L * / 0 F a 3^* 6 E * I * / - 81 sys

x f.1 F x * a L - (x 2^* a a a 3 L * - (* 2 L 2^* + (* + (* 6 E * I * L * /

x f.2 F a * x a 2^2 L 2^* + x x 3 L * - (* + (* a 2^L * - (* 6 E * I * L * /

f.max x f.1 x L 2 / ≡ a L 2 / ≡ 21 sys at : F L 3^* 48 E * I * /

Sanity check, this is the expected result for a simply supported beam with concentrated force in the center

S x f.1 x diff x x.0 ≡ at 0 ≡ x.0 Solve :

S x.0 a a - 2 L * + (* sqrt 3 sqrt / - ≡ x.0 a a - 2 L * + (* sqrt 3 sqrt / ≡ 21 sys

Search for the extremal point in f.1, thus assuming that F is shifted to the right of the center, such that the maximum deflection will occure in range 1,

S 2 el Assign a a - 2 L * + (* sqrt 3 sqrt /

x.0 f.1 F 32 nthroot 3^* a L - (a a - 2 L * + (* sqrt 3^* 3 a * a a 3 L * - (* 2 L 2^* + (* a a - 2 L * + (* sqrt * + (* 162 E * I * L * /

x.0 f.1 f.max / a 34 / L * ≡ at Maxima 0.6988

w.1 x L * f.1 f.max / Maxima : 8 x * L 2^a L - (* x 2^* a a a 3 L * - (* 2 L 2^* + (* + (* L 3^/

w.2 x L * f.2 f.max / Maxima : 8 a * x L 2^23 - x + (x * + (* a 2^+ (* a 2^- (* L 3^/

a 78 / L * :

L 1 :

w.1 x 0 a ltlt / w.2 x a L ltlt / 2 1 sys