Question

Please answer all parts to the question

n = 0

Start writing on a new calculations page. A pin Jointed truss ABC is made from three 100 mm long members pin.jointed at their ends. A horizontal force Fy is applied at B. B F 100mm loomm А 100mm C Use Castigliano's theorem to calculate the VERTICAL displacement of Joint B. Use the following values for the parameters: 2 Every member has a cross section of A-200 mm Every member hos a Young's modulus of E - 80 GPA The values of force Fy is given in k by F-(20 + n) kN

Answer 1

A horizontal force (fa) applied at'B. Solution:- A pin jointed touss 'ABC', shown in fig(e) F1 known: - Joomm 100mm Cross section A с 100mm young's VRA tre length of each member = 100 mm (L) geach member 300mm (A) 토서 's modulus (E) = 80GP9 fig(1) 0.86694 0.866f1 Analysis: - : - Reaction forces at A and C can be calculated first we have to find out forces in each members. Assumption:- rigid. Now, by point Method; - at point @'; FBC fbe=fal =f- A I easily. All members are FA . AB (20 120 B 120 at point ac' FAB FAC= foe C0360 = A costo 0.866 F FAC ferien Fae = 0.561 FBC We know strain eners energy (E) force (P) ; Es of a ês a member due to cial pa L 2.AE C scanned with CamScanner

So, strain Energo FABL 24E u Pogle 24E 2AE 0.85632 2.AE u = Freže = LAE → Total strain Energy of or 1-0 (giren) 80, fi= 20 kN- 20000 N. Energy of member (AB); E AS 9.AE (BC) - Ese = PL (CA) – Ene Ene whole fruss (E) = East Epet EAC RAL 0.25G²L E = + JAE NOW, By Castiglliano's theory af So, ӘE 2.as ( al 2-25 FIL af LAE AE 2:25 ft (100)= [1.40625 Xlo®] F. SB (2001 ( 80x103) (20 th) kN ; (given) FEL AE + 2.2562 QAE QAE DE fe ad ㅠ 3 z .: F Value FE ; in Egi(5 g putting By GB = 0.28145 mm Ansiz CScanned with CamScanner