Question

UTILEEP ' S The young tree, originally bent, has been brought into the vertical position by adjusting the three guy-wire tensions to AB = 3 lb, AC = 15 lb, and AD = 18 lb. Determine the force and moment reactions at the trunk base point O. Neglect the weight of the tree. 4.8' OT- mi 3.2" 5.0 5.0'yo * 3.2 Answers: k) lb Fo=1 i Mo=1 i j + i k) lb-ft Attempts: unlimited Save for Later Submit Answer

Answer 1

B (0,-5,0) C(3-2,5,0 D 1-3-2, 5, 0) A (0, 0, 4-8) AB 2 3 lb ; AB a ob-on AC = 1516 ; AD 2 18 16 = (-5% -4.8 %) tt AR .8k = -0.72138 j - 0-6925318 i 231 s? +.32 Ãc z oc-oi = (3.2 i + sŷ -4.8 ů ft C = Ã ć. 3-2 i tŷ -4-5 Å ZOMuAou i + 0.6985 i = 0.67056ie LACI 3.22 +5² + y² ÃO = OD 5a = -3-2 ir sj _4.8" ÂD E DA A -3-21 +S) -4.8K = -0.44704 + 0-6485 ) - 0.670SLK J 3-1 +52 +4-32 i ot = 4.8 ". H - T, T2, T3 tensions in AB, AC AD respectively . Tia 31b: Tz = 15 lb ; T3 = 18.16 F = T. AB = 3. AB = (-2-16414 ŷ - 2.877595 ů) ab r = Tz- Ar z 15. Rc = (6-7056 i + 10.4975i - 10-05 su ů) is T = Tz-ÂD = 18-AD +(+8-04672 i + 12.573 Ï - 12.07008 ) eb

. tree if i is the reaction force at support o' then equilibrium of forces and this given by Ef=0 PS + Tith T3 =0 (to - (I + P + Tz) = (+1:34112 i 20-88636 ŷ + 24.206075 ů) ab equilibrium of moments about to it ño is the reaction moment at o . EM 20 Mo + ot x T + 5A x T2 + OA X G =0 ño =-0A x (Tit. Iz tij) = oA x [(T + E +13) z ot x to z u- 8² x (1.3412a - 20-88631; + 24-20 60756) lb-ft ño I (4-8 x 1-34112) (uxi) -(4-8 * 20-8838) (kx)) z (8.437776 j - 100-24128 î) lb-ft , Mo = (-100.24128 î + 6-437376 ŷ to ê ) 1b-4)