b73687b9-d323-4bc8-ae0f-eec47d274953 29 overlord Oscar Campo 4 5 false false 0 7 decimal

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L 10 in * :

a 4 in * :

w 10 kip in / * :

Definition singularity function:

xx aa nn fsin f xx aa - (nn^xx aa > (* nn 0 ≥ (* : dummy f 0 ≈ f 0 : if 11 line : f 31 line :

x q R.1 x 01 - fsin * w x a 0 fsin * - R.2 x L 1 - fsin * + :

x V R.1 x 00 fsin * w x a 1 fsin * - R.2 x L 0 fsin * + :

x M R.1 x 01 fsin * w 2 / x a 2 fsin * - R.2 x L 1 fsin * + :

Boundary condition, on x>L , V(x) and M(x) are zero

x# L 1010 -^in * + :

x# V 0 ≡ x# M 0 ≡ 21 sys R.1 R.2 21 sys Solve Assign kip #

x# V 0 ≡ x# M 0 ≡ 21 mat R.1 10 kip * ≡ R.2 10 kip * ≡ 21 mat FindRoot kip 184221 mat

x in * V x in * M 2 1 sys

Mmax 5.8 in * V : kip 6.7136 1013 -^* -

For elastic tangent, we use θ(x) and y(x)

x θ 1 E I * / R.1 2 / x 02 fsin * w 6 / x a 3 fsin * - R.2 2 / x L 2 fsin * + C.1 + (* :

x y 1 E I * / R.1 6 / x 03 fsin * w 24 / x a 4 fsin * - R.2 6 / x L 3 fsin * + C.1 x * + C.2 + (* :

I π d 4^* 64 / :

E 30000 ksi * :

d 2 in * :

Boundary conditions: y(x) is zero on supports

0 y 0 ≡ L y 0 ≡ 21 mat C.1 100 - (kip * in 2^* ≡ C.2 0.01 - (kip * in 3^* ≡ 21 mat FindRoot kip in 2^* 246 - 2.2794 106 -^* m * 21 mat

0 y 0 ≡ L y 0 ≡ 21 sys C.1 C.2 21 sys Solve Assign kip in 2^* #

C.1 kip in 2^* 246 -

R.1 kip 18

plotting elastic curve y(x)

C.2 kip in 3^* 8.9739 105 -^*

R.2 kip 42

x in * y x 0 ≥ ( x 10 ≤ ( & ( *

To find point of maximum deflection we use θ(x) = 0

x in * θ x 0 ≥ ( x 10 ≤ ( & ( *

The plot shows that the point where θ(x) = 0 is between 4~6

x θ Unknowns x 11 mat

Trying to find the exact point of max deflection (xm)...

x in * θ 0 ≡ xm Solve Assign #

xm x in * θ 0 ≡ x 46 solve : 5.2638

x θ 0 ≡ 5 in * FindRoot in 5.2662

xm x in * θ 0 ≡ x 46 solve : #

x equ x in * θ :

xm x in * θ 0 ≡ x solve maple : #

x f x 1 el equ :

411 mat 01015 -^f al_nleqsolve 5.2638 11 mat

x in * θ 0 ≡ xm 4.5 ≡ FindRoot #

x in * y x 0 ≥ ( x 10 ≤ ( & ( * xm 0.00092 - | 10 red 1 5 mat 2 1 sys x in * θ x 10 0 gege ( * xm 00 o 10 red 1 5 mat 2 1 sys