ASE 365 HW 1 Solutions

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Lone Star College, CyFair *

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Course

365

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Electrical Engineering

Date

Oct 30, 2023

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pdf

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6

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1) F80 /2) coordinate system O it Io " M Ix ↓ 01 r / ↓ my T Es 3 as compatibility x = r bi = ro -> k = ri - i = r 6) Constitutives Law Fs = k x C Equilibrium [Mo-5 . -Fir= Io8 Io = M T = E + Fs [Fx = my - T = mi my - (20 + kx) = mi mi + (E) + kx = my (m + 2) + kx = my Key = K
2) eI 1) FOU /2) coordinativ ~ ⑧ k2 ↑ Fs , A O Ox - Fsz - Toy ↓ It * -> nee m Ix Fs , ↓ t -- my 3) a) compatibility SA = a Sint = GO 30 = bsi8 = 60] given &< 6) Constitutive Laws Fs , = k , (2 - AA) = k , (X - a) * assuming < at Fsz = kz (18-0) = kebO c) Equilibrium [Mo= Fs , a- Fs2 . 6 = 0 [Fx= my- Es , = mi k , (X - a) . a - (k - bt) . b = 0 my - k , (X-at) = mi using ak , X - k , a - k2628 = 0 my - K , x + k , "a x = mi ak , = (k , a 2 + K2 62) 8 (k , a + k26) G = k , a X (k , a + k2b20 mi t I K , - Ka I X = my (k , a + k2b2)
mi + /k , CK , a +Ke6Y) - Kia I x = my (k , a + k262) m + KIK262 x = my (k , a + k=b2) Reg = K , K2 62 (1x , q2 + kzb2)
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3) 1) Fr0/2) Coordinates - -me e 1 F ~ ~ in ~ ~ Es 2 * Es ~ It ↑ R ~ / o it - 0 A my r = 1 2 3) a) Compatibility x = (v + a) Sint = (U+a)8 6) constitutives Lams Fs = k x = k(r + a) C) Equitiku SMA= my . r8-2Fs . (Ura)= It my UF-2 k(r+a)2 8 = ( * + mrr) Imr2 + (2k(rta - mgr)8 = 0 Req = (2 K(r+al2 -myr)
4) 1) F80/2) Coordinates - Fr / E E F ~ E IA = I (m - 2) 2 ~---- Im A(e)g ⑤ 3) a) compatibility * = I Mint O b) constitutives Law Fs = kx = k = 0 es Equilibrium Me [MA = (4q(=0) - 2 . Fs(z) = In -2 . Ko = ! mel" I st j + I - m(8 = 0 I 3 Keg K - 2 my 2
9) FOO : a) M k ↓ E ↓ F ~ ↑ ↑ 1 y ↑ E k , = I ~ //// from beam equation : EI W"(x) = Fx 8 =x EF Wix) = + A fram &C : W(I = 0 , wI(L7 = 0 : EIw(x) = I + Ax + b = >A = - F(2 ! - E E ⑧ - 2 W10) : F = y ⊥ 3 EE constitution Laut F = ~ E . y Fs , = k , y L * given batt springs have "equal" displacement thes are is parallel : ↓ F ky =F - No Key = k6+ K , = + K b) E IX1 constituti Lams F , , Fr = F ! xz I * Given the younge have "enquential" displacements . " ce - I s so , ↓ = E kea + I ki Keq ↓ F
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