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83500294-bc17-4223-b4f4-0193a97e3a96 184 4 5 decimal

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Continuous Beam, with Two Unequal Spans, Unequal, Uniform Loads

Machinery's Handbook 30th Edition table 1 case 21

I 0.0002 m 4^* :

E 30 GPa * :

L.1 4 m * :

L.2 4 m * :

q.1 50 kN m / * - :

q.2 4 kN m / * :

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Hjelpedefinisjoner

Q.1 q.1 L.1 * :

Q.2 q.2 L.2 * :

L L.1 L.2 + :

Oppleggskrefter og enderotasjoner

R.A Q.1 L.1 * 3 L.1 * 4 L.2 * + (* Q.2 L.2 2^* - 8 L.1 * L * / :

R.B Q.1 Q.2 + 2 / 18 / Q.1 L.1 * L.2 / Q.2 L.2 * L.1 / + (* + :

R.C Q.2 L.2 * 3 L.2 * 4 L.1 * + (* Q.1 L.1 2^* - 8 L.2 * L * / :

θ.A 4 R.A * Q.1 - (L.1 2^* 24 E * I * / - : ° 0.9804

θ.B 8 R.C * 3 Q.2 * - (L.2 2^* 24 E * I * / - : ° 0.6875 -

θ.C 4 R.C * Q.2 - (L.2 2^* 24 E * I * / : ° 0.3947

Funksjonsuttrykk for skjærkraft og bøyemoment

x q q.1 x 0 L.1 lelt q.2 x L.1 L lele 0 cases :

x V R.A q.1 x * - x 0 L.1 lelt R.C - q.2 L x - (* + x L.1 L lele 0 cases :

x M R.A x * q.1 2 / x 2^* - x 0 L.1 lelt R.C L x - (* q.2 2 / L x - (2^* - x L.1 L lele 0 cases :

Funksjonsuttrykk for helning og utbøyning

x θ x' L.1 x - : x' - 2 L.1 * + (Q.1 - 4 R.A * + (* L.1 * Q.1 L.1 x' - (2^* - (L.1 - 2 x' * + (* - x' L.1 x' - (* Q.1 - 4 R.A * + (L.1 * - 2 L.1 x' - (* Q.1 * + (* + 24 E * I * L.1 * / 21 line x 0 L.1 lelt x' x L.1 - : x' - 2 L.2 * + (Q.2 - 4 R.C * + (* L.2 * Q.2 L.2 x' - (2^* - (L.2 - 2 x' * + (* - x' L.2 x' - (* Q.2 - 4 R.C * + (L.2 * - 2 L.2 x' - (* Q.2 * + (* + 24 E * I * L.2 * / - 21 line x L.1 L lele 0 cases :

x w x' L.1 x - : x' L.1 x' - (* 24 E * I * / 2 L.1 * x' - (4 R.A * Q.1 - (* Q.1 L.1 x' - (2^* L.1 / - (* 21 line x 0 L.1 lelt x' x L.1 - : x' L.2 x' - (* 24 E * I * / 2 L.2 * x' - (4 R.C * Q.2 - (* Q.2 L.2 x' - (2^* L.2 / - (* 21 line x L.1 L lele 0 cases :

Bestemmelse av karakteristiske snitt

zero shear span 1

x.1 R.A q.1 / : 1.77 m *

zero shear span 2

x.2 L R.C q.2 / - : 3.125 m *

zero slope span 1

c.a q.1 6 E * I * / - :

c.b R.A 2 E * I * / :

c.c 0 :

c.d θ.A :

x.3 c.d c.c c.b c.a 41 mat polyroots m * : 1.3592 m * - 1.9011 m * 4.7681 m * 31 mat

c.d c.c c.b c.a 41 mat 0.0171 0 0.0074 1 m 2^/ * - 0.0014 1 m 3^/ * 41 mat

zero slope span 2

c.a q.2 6 E * I * / - :

c.b R.A 2 E * I * / R.B 2 E * I * / + Q.1 6 E * I * / 3 * - q.2 6 E * I * / 3 * L.1 * + :

c.c R.B 2 E * I * / 2 * L.1 * - Q.1 6 E * I * / 3 * L.1 * + q.2 6 E * I * / 3 * L.1 2^* - :

c.d θ.A R.B 2 E * I * / L.1 2^* + Q.1 6 E * I * / L.1 2^* - q.2 6 E * I * / L.1 3^* + :

x.4 c.d c.c c.b c.a 41 mat polyroots m * : 5.7628 m * 6.3228 m * - 9.9349 m * 31 mat

scale\0020\slope 100 :

scale\0020\deflection 4 :

x m * q kN m / / x m * V kN / x m * M kN m * / - x m * θ ° / scale\0020\slope * x m * w mm / scale\0020\deflection * - 5 1 sys x m * θ ° / θ.A R.A 2 E * I * / x m * ( 2 ^ * + q.1 6 E * I * / x m * ( 3 ^ * - ° / θ.A R.A 2 E * I * / x m * ( 2 ^ * + R.B 2 E * I * / x m * L.1 - ( 2 ^ * + Q.1 L.1 L.1 3 x m * L.1 - ( * + ( * 3 x m * L.1 - ( 2 ^ * + ( * 6 E * I * / - q.2 6 E * I * / x m * L.1 - ( 3 ^ * - ° / 2 1 sys

Slope equation (cubic) and its roots

θ.A ° 0.9804

x.3 m 1.3592 - 1.9011 4.7681 31 mat

x.4 m 5.7628 6.3228 - 9.9349 31 mat

θ.B ° 0.6875 -

θ.C ° 0.3947

x m * θ 0 ≡ x 0 L solve m * 1.9011 m * 5.7628 m * 21 mat

Notice that the solutions from polyroots corresponding to the solutions from the solveblock change it's place within the solutionvector from polyroots when the value of q.2 (input) changes from 4 to 5 You can observe from the plot on the lower right that the solution is root nr. 2 This makes it difficult to "hardcode" the solutions in the final programming, in which I dont want to use a numerical tool like solve().

sol_1 θ.A R.A 2 E * I * / x m * (2^* + q.1 6 E * I * / x m * (3^* - ° / :

sol_2 θ.A R.A 2 E * I * / x m * (2^* + R.B 2 E * I * / x m * L.1 - (2^* + Q.1 L.1 L.1 3 x m * L.1 - (* + (* 3 x m * L.1 - (2^* + (* 6 E * I * / - q.2 6 E * I * / x m * L.1 - (3^* - ° / :

x f sol_1 :

x q sol_2 :

x Φ1 x f parfrac x convert maple :

x Φ2 x q parfrac x convert maple :

sol_1 sol_2 2 1 sys

x expr x Φ1 op maple :

x Φ1 x 3^4 π * / 531 x 2^* 400 π * / - 7725 π * / +

x 1 :

u x expr reverse :

# op maple is undocumented in Mathcad 11 and earlier ≡

x expr x Φ2 op maple :

x 1 :

v x expr reverse :

The 'x' term is absent
thus can't be automated
fill-in manually.
Same in Mathcad u 0.980394 0 0.422556 - 0.079577 41 mat :

v 2.3046 - 0.2674 0.0597 0.0064 - 41 mat

r u polyroots : 1.3592 - 1.9011 4.7681 31 mat

ρ v polyroots : 5.7628 6.3228 - 9.9349 31 mat

x f1 x r n el - (n 13 product :

x f2 x ρ n el - (n 13 product :

u 4 el x f1 * v 4 el x f2 * 2 1 sys x f x q 2 1 sys