Question

Consider the frame shown in (Figure 1). EI is constant. Part A Determine the y component of reaction at A. Express your answer to three significant figures and include the appropriate units. -0% Ti A ? Ay = Value Units Submit Request Answer Part B Determine the component of reaction at C. Express your answer to three significant figures and include the appropriate units. igure 1 of 1 НА ? 6 m 18 kN/m C = Value Units B Submit Request Answer 4 m Part C Determine the y component of reaction at C. Express your answer to three significant figures and include the appropriate units.

Answer 1

Since at support A beam is simply placed over I section .hence I have taken hinge support at A.

Please do comment in the comment section if it is not so.I will solve then other way taking roller support or fixed support as the actual case would be.

Given data, EI = Constant W 2 18 kN/m (8KN/m A B Hinge to HA RA To find? RA Rey Hc) Mc? Exed Mc >kie Rc

no. of Ds - 8= No. of D. Stepl: Calculation of static Indeterminacy (P.): 3m +8-3j mano, members. reactions. = No. of joints. Ds = 3x2 +5=3x3 =2

So As Ds >0 ie the beam is indeterminate we will require compatibility equations & in addition of equilibrium equations (Efco, {fyzo, EM=o) to find unknown support reactions, Moment Distribution Method using Let's solue Step 2: Calculation of Distribution Factor (DF) Stiffness Member Total stiffnes Joint 13 BA ISEI B SET - OSEI IBA 4 EF = Ef ape 2/3 B C

Step 3: Calwlations for Fixed End Moment (FEM): "A B MFBC MEAB MEBA MECB 2. MEAB Wl? -18862 30 30 =-21.6kNom Sign Convention Clockwise moment tive Anticlockwise moment: five we? MEBA=+ = 18x6² MEBC = MECB=0 20 32.4 knom Step 4: Moment - Distribution Table B 4 TV3213 21.6 '32.4 o el DF 0 FEM +21.6 10.8 Final FEM 43.2 - 14-4 1-2818 Balance >-14.4 Carry Over 28.8 -28.8 -14.4 Final Moment { 0-③

* → As support A will not resist moment (ie MA=o). So we applied Counter moment at support A to make net moment at A=0. Carry over to moment from B to A will not be there because A support A will not resist moment. Carry عمران value is half of the mon oment in the the same direct sense, applied and Pa

Step 5: Draw Free Body Diagram (FBD): = 28.8K Nom MBA at t w B q > He •HA RC Rc Hc RA MBC =~28.8 KN-m () ) Me =-14.4 KN 1. Ис "Ro

Step 6: Support Reactions calculations: for span AB SMA=0 Rc X 6 - 28.8 x6x 18 x 2,6 40.8KN Ans. { Fv so Ratke = { x 6 x 18 = 54 54-Re = 59-40.8= J13-2 KN. 13.2 KN. An THA==Hel For span BC RAS EFM o R HAT He to Take Moment about c. Hex 4+28-8 +14.40 Ans. >/16 -/0.8 KN IHA=+10.8kN Tive sign of He indicates that our assumed you is incorrect and it will act opposite of that. direction