Question

please disregard work

For the structure shown below, using the FORCE METHOD determine the reactions at A and at C when a distributed load w =6 kN/m is applied on the column and concentrated load P=20 kN applied on the beam as shown. (Moment of inertia for the beam is 2xl and for the column is 3xl same material. E= 200 GPa and 1 = 240x106 mm. A is a built-in support, the members are rigidly connected at B and point C is a PIN support (Shear and axial deformations are negligible). [HINT: You can borrow information from Problem 1, clearly indicating which information you are borrowing and explain WHY you can borrow the particular result Find A., Ay, Cx, ly 6 m 3.1 2.

Answer 1

Solution; Criven STRUCTURE : 20KN 2 r zm pa the we KNOW THAT STORED ↑ Strain Energy'u i mida J ZEI rding to Castiglian -o's ACC 11 Sn = jm m du CHE Ò Es Where, e length of Member. My > B.M at x-x due to applied wad m=2 Me - Bim at xnx due to unit Horizontal load at the point where Hosizontal displacement is calculated spreet with Horizontal displacement. am Scanner

i koko noun k nim. value: - Mx - Value: Mrim dhe Member Mx m ? (unc-40+ He) (-2) IVAY-20x2 thern Now = Horizontal displacement at in = Elmaim dre Plure -40% she) (-x) dhe Scanned with CamScanner E (31)

Since, Horizontal displacement at 'c' is Not possible due to pin support at e - ol Compatibility Condition] Ituvert yos - x? Heldre a o BEI 31 [-2 ve 26² +20*6²-Hex 6²] = 0 -72V-72he =-720 Vet He = 10 - Ev=o ♡ VAI Vc = zokn си со HA+Hc = 6*6= 36 kN -∞ Due Symmetry of Horizontal loading on span 'ABB CamScanner = He Scanned with

from equation ③ THA= He = 36 = 18 kr (E), Ans → from eano : Ve=1o-Hc = lon8=-8kN Nott he sign shows that Ve is opposite to the assumed direction of Ne [Ve=8kw (W) Ans > from equ o VAT(-8)=20kn V=28 Kor (1) Ane > Taking moment at 'A "Ć Moro [Due to pinned at &] NA*4 & HA*6 --(3643) - MA -20%2=0 (28*4) + (18*6)-(36*3) - 2002) = MA IMA = 72kr-m (1) Ane Scanned with CamScanner