Question

3. Find the deflection at B by Castigliano's Second Theorem. Express your answer in terms of P and EI. (25 Points) 5P А C 21 B L/2 L/2

Answer 1

БР А سا 21 B I ☆ 42 4/2 if Ос calculate the reaction In this case at RA & RB Take moment at A Rex L 5 P X JH 2) Rc 5 Р 2 x RA + Rc = 5P 2) RA 5P-51 5P 2 5P . RA 5 P 2 G Rc 5 P 2 from the equilibrium of forces we calculate the moment MAB MBC MAB RAR 52 xx БРx MBC = Rea 2

strain energy. M2 da u 2EI 1/2 UAB = Ex(21) s (5px =) de 1/2 1 25 px LEI da 4 42 х 3 28 x pm [ Х 4E1 25 16 EI ph x 1 x х Х 3 = 25PL 3 84 FT Similarly 1/2 UBC (5P²) de 2 EI 23942 11 26 x 25 pk x 2 EI o 25 pm N x ţ x 8 ET 25p2 L 192 EI 3 ". Total, u 11 UAB + UBC 2 250m2 (5 + ) ΕΙ 75p2² 384 FT U

is the orcem. Castigliano's do du - de 3 d 75 PVL 384 FI de L3 75 384 Х x 2p EI SB = 150 PL? 384 EI 150 PL3 ... deflection at B is 384 ET