Question

A propped cantilever beam with length an is subjected to a trapezoidal load with intensities, 2018 and 9,- 30 kN/m Find the reactions at A and B. Hint: The loading is the sum of uniform and triangular loads. (Enter your reaction forces in kN and your reaction moments in KN · m. Solve this problem by the method of superposition. This beam has constant flexural rigidity El. Assume that the +x-axis is to the right, the +y-axis is up along the page, and the +z-axis is out of the page. Use the statics sign convention.) RA KN KN MA KN.

Answer 1

2p % 90=20 kolm B Quis 30 kaolm A Do L = 3 L By Super position principle: Above one can be di vide dento 3 parts. (4,-9.) 20 Ton B B + В RB L y 10 B is zero. Such that net deflection at Sot &"bt ies SB so %0.24 SEI 8" -( - - ) B 11 30 EI S lla). <3 3 ET

. Core4 19,-90), 14 RB . 18 8 E ЗЕТ 30.t -(20)(3) ( 30-20)(34) (Re) (3) 2 3 8 30 KN t Reaction at B. RB = 28.5 Simplified view.30 25.5 KN frog INS Statics sign convention 3 30 2 (M5 125.5 Stress/statics Sign conventim equivalent Concentrated load for trape-roid load pa 15 x 3 x 10 of 20x3 KN Pr auts Ith of total length from left acts at center. A

Pi Pr MA TRA Parol 42 나 Po - Pr 7 Sfyzo Ay + RA -25.5+75 Ay . & Ans. RA 49.5 KN Ay EM >> @A - MA-11, 1X143) - (83 x 42) +RAXL) - MA (155*1) + (60) (13/1) - (25.5X3) - 28.5 Knim * Ans. (with sign) ܘ .ܐ MA 28.5 knim Counter clockwise Ahorst Choisit static Sign conversion)