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´Ü¼øº¸¿¡ ÁýÁßÇÏÁßÀÌ ÀÛ¿ëÇÒ ¶§ º¸ÀÇ Ã³Áü½Ä
[ 2019-11-24 21:08:38 ]
±Û¾´ÀÌ  
metalheart
Á¶È¸¼ö: 4575        

±×¸²°ú °°ÀÌ ±æÀÌ°¡ L (m) ÀÎ ´Ü¼øº¸¿¡ ÁýÁßÇÏÁß P (kN) ÀÌ ÀÛ¿ëÇÒ ¶§ º¸ÀÇ Ã³Áü·® vx (mm) À» ±¸ÇÑ´Ù.
P ÀÇ ÀÛ¿ëÀ§Ä¡°¡ A ÁöÁ¡¿¡¼­ Lp (m) ¶ó¸é, A ÁöÁ¡¿¡¼­ÀÇ ¹Ý·ÂÀº RA = P*(L-Lp)/L °¡ µÇ°í, B ÁöÁ¡¿¡¼­ÀÇ ¹Ý·ÂÀº RB = P*Lp/L ÀÌ µÈ´Ù.
A ÁöÁ¡À» ¿øÁ¡À¸·ÎÇÏ¿© x (m) ¸¸Å­ ¶³¾îÁø À§Ä¡¿¡¼­ ¸ð¸àÆ® Mx (kN-m) ¸¦ ±¸Çϸé,
x ¡Â Lp ÀÏ ¶§, Mx = RA*x = (P/L)*(L-Lp)*x
Lp ¡Â x ÀÏ ¶§, Mx = RB*(L-x) = (P*Lp/L)*(L-x)
°¡ µÈ´Ù.

E*I*v¡È= Mx ÀÇ °ü°è°¡ ÀÖÀ¸¹Ç·Î, À̸¦ µÎ ¹ø ÀûºÐÇϸé,
x ¡Â Lp ÀÏ ¶§,
E*I*v = (P/L)*(L-Lp)¡óx dx
     = (P/L)*(L-Lp)¡ò(1/2)*x^2 + C1 dx
     = (P/L)*(L-Lp)*((1/6)*x^3 + C1*x + C2)
x = 0 ¿¡¼­ vx = 0 À̹ǷÎ, C2 = 0
E*I*v = (P/L)*(L-Lp)*((1/6)*x^3 + C1*x)
ÀÌ µÇ°í,
Lp ¡Â x ÀÏ ¶§,
E*I*v = (P*Lp/L)¡óL-x dx
     = (P*Lp/L)¡òL*x - (1/2)*x^2 + C3 dx
     = (P*Lp/L)*((L/2)*x^2 - (1/6)*x^3 + C3*x + C4)
x = L ¿¡¼­ vx = 0 À̹ǷÎ, C4 = -C3*L - (1/3)*L^3
E*I*v = -(P*Lp/L)*((L/2)*x^2 - (1/6)*x^3 + C3*x - C3*L - (1/3)*L^3)
ÀÌ µÈ´Ù.

x = Lp ¿¡¼­, ±â¿ï±â°¡ °°À¸¹Ç·Î,
(P/L)*(L-Lp)*((1/2)*x^2 + C1) = (P*Lp/L)*(L*x - (1/2)*x^2 + C3)
(L-Lp)*((1/2)*Lp^2 + C1) = Lp*(L*Lp - (1/2)*Lp^2 + C3)
C1*(L-Lp) = L*Lp^2 - (1/2)Lp^3 + C3*Lp - (1/2)L*Lp^2 + (1/2)Lp^3
¨ç C1*(L-Lp) = C3*Lp + (1/2)L*Lp^2
ÀÌ µÇ°í, x = Lp ¿¡¼­, óÁü·®ÀÌ °°À¸¹Ç·Î,
(L-Lp)*((1/6)*Lp^3 + C1*Lp) = Lp*((L/2)*Lp^2 - (1/6)*Lp^3 + C3*Lp - C3*L - (1/3)*L^3 )
(L-Lp)*(Lp^2 + 6*C1) = 3*L*Lp^2 - Lp^3 + 6*C3*Lp - 6*C3*L - 2*L^3
6*C1*(L-Lp) = 3*L*Lp^2 - Lp^3 + 6*C3*Lp - 6*C3*L - 2*L^3 - L*Lp^2 + Lp^3
6*C1*(L-Lp) = 2*L*Lp^2 + 6*C3*Lp - 6*C3*L - 2*L^3
3*C1*(L-Lp) = -3*C3*(L-Lp) + L*Lp^2 - L^3
ÀÌ µÈ´Ù.
¿©±â¿¡, ¨ç À» ´ëÀÔÇϸé,
3*C3*Lp + (3/2)L*Lp^2 = -3*C3*(L-Lp) + L*Lp^2 - L^3
3*C3*L = -(1/2)L*Lp^2 - L^3
C3 = -(1/6)Lp^2 - (1/3)L^2
À̸¦ ¨ç ¿¡ ´ëÀÔÇϸé,
C1*(L-Lp) = -(1/6)*Lp^3 - (1/3)L^2*Lp + (1/2)L*Lp^2
C1*(L-Lp) = (1/6)*Lp*(- Lp^2 - 2*L^2 + 3*L*Lp)
C1*(L-Lp) = (1/6)*Lp*(L-Lp)(Lp-2L)
C1 = (1/6)*Lp(Lp-2L)
ÀÌ´Ù.

C4 = -C3*L - (1/3)*L^3 À̹ǷÎ,
C4 = (1/6)L*Lp^2 + (1/3)L^3 - (1/3)L^3 = (1/6)L*Lp^2

µû¶ó¼­, ±¸°£º° v ´Â ´ÙÀ½°ú °°´Ù.

x ¡Â Lp ÀÏ ¶§,
vx = (P/(EIL))*(L-Lp)*((1/6)*x^3 + (1/6)*Lp(Lp-2L)*x)
  = (P*x/(6EIL))*(L-Lp)*(x^2 + Lp^2 - 2*L*Lp)

Lp ¡Â x ÀÏ ¶§,
vx = (P*Lp/(EIL))*((L/2)*x^2 - (1/6)*x^3 + C3*x + C4)
  = (P*Lp/(EIL))*((L/2)*x^2 - (1/6)*x^3 - (1/6)Lp^2*x - (1/3)L^2*x + (1/6)L*Lp^2)
  = (P*Lp/(6EIL))*(3*L*x^2 - x^3 - Lp^2*x - 2*L^2*x + L*Lp^2)

ÇÑÆí, Lp = L/2, x = L/2 ÀÏ ¶§, óÁü·®ÀÌ ÃÖ´ë°¡ µÈ´Ù.

x ¡Â Lp ±¸°£ ½Ä Àû¿ë,
vx = (P*x/(6EIL))*(L-Lp)*(x^2 + Lp^2 - 2*L*Lp)
  = (P/(12EI))*(L/2)*((1/4)L^2 + (1/4)L^2 - L^2)
  = -(P/(48EI))*L^3

Lp ¡Â x ±¸°£ ½Ä Àû¿ë,
vx = (P*Lp/(6EIL))*(3*L*x^2 - x^3 - Lp^2*x - 2*L^2*x + L*Lp^2)
  = (P/(12EI))*((3/4)*L^3 - (1/8)L^3 - (1/8)L^3 - L^3 + (1/4)L^3)
  = (P/(12EI))*((3/4)*L^3 - L^3)
  = -(P/(48EI))*L^3
guest1 ÇÏ... ÀÌ°É... ´«¾Ë ºüÁú µí.... ¾ÏÆ° µµ¿òÀº µÇ³×¿ä. 
[2019-11-25 04:16:18]


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