Question

I need the solution please. The answers for these questions are:

HA =63.66kN

Maximum hogging =166.9kNm ( occurs at $\theta$=32.48 degrees to horizontal)

Max sagging moment = -327.1kNm at mid span

Point of contraflexure at  $\theta$=64.96 degrees

Question 2 (25 marks) The semi-circular two-pinned arch ABC shown in Figure Q2 is pinned to rigid foundations at Positions A and C. The flexural rigidity (EI) of entire length, and its diameter is 18m. arch rib is constant throughout its The arch supports a single concentrated vertical load of 200KN at its apex (Position B). The self-weight of the arch can be ignored in the analysis. a) Using an energy method of analysis, calculate the magnitude and direction of the horizontal reaction at the support at Position A. (15 marke) Determine the positions and magnitudes of the maximum hogging and sagging bending moments within the arch rib, and the positions any). b) f points of contraflexure (if (10 marks) 1200 kN B 9 m 18 m Figure Q2 One or more the following relationships may be useful: sin 28 2 sin 28 (cos e) 8e -(sin e fcos e sin e 8e contd

Answer 1

00 kn PCr,y doo kns 18 m 1 R Spe . Due to hymmety Haizontal reation ( H) - = l0 kN. RA = RB My ds ds=R de T 2 M ds Mo ds C 0 . CReade) T/2 Mo Rde WCR-R Sm - wR (1-Sme) MD 11 ds Moy Cm co do - cos de dt t 1-met tdt) WR Moy ds R de ds T2 3 TRYZ WR3 H xTR T

M-ve)m (M+w max 'ma ReMD Marimum hagging moment will accurs at croun Re x R- HxR 100x963. 66 xR Wen 3. M in ib AB hx H-x hunb (R-R case) M 100 63.66 x R&m 00 R (OA- 400 (-cose) bnding Chogging mement -de 63.66XR Bm dM O F31 mau tano= 900 3.4 - 57d.94 Sn(32. 48) g00 cos(32419)) -166.89 kN-m M pont ofcontha tlure, M= 0 above equation Scving