Question

Members ABC and BD of the counter chair are rigidly connected at B and the smooth collar at D is allowed to move freely along the vertical slot. a) Draw the shear and bending moment diagrams for member ABC. b) For the given cross section for member ABC determine the centroid and the moment of inertia (1) with respect to Neutral Axis c) If the maximum bending moment is 225 lb-ft, determine the maximum absolute bending stress and its location along the member ABC. P = 150 lb 14 1.5 ft 1.5 1.5 ft 11 in 2 in 1 in 6 in 3 in 4 in

Answer 1

page solution. Equations of Equilibrium: Referring to the free - body diagram of the frame shown in fig @ Iself ti Efy losit los fat - Ay G+EMA = 0; -0, Ay - 150 20 Ay= 150 lb No (105)- 150(3)=0 Ng = 300 lb. An losft fig@ Isoll 1.5 ft Ay Shear and moment diagrami The couple moment acting on l.sft B due to Ng is Mg = 300x1.5 = 450 lb-ft. The loading acting on member ABC is shown in fig@ and the Shear and moment 3oolb diagrams are shown in fig © and fig. Vilb) do ph MB 2450lb.ft fig (6. Mlebuff) Iso 225 los X (ft) 1.5 figo - 225 Area of section(A) fig@ - lxy - 4 in? Tuin y, a sos in Area of section 2 (A2) = 2x2 42 in jin 2 in lbin = 4 in? = 4 in Y2 = 3+2 teş 3 in K u in.

pag . for section 3 (A3) = 3x4 = 12 in2 Y3= los in. 3 y = 1 Aly, + A2y + A343 Ai + Azt A - 3 4x sist 4X4 + 12x lis 4t u + 12 odl 56 20 2.8 in. Ans Scho y for section to I 4 x 2² 11 bd² 12 4 in = 0.333 in 4 12 Ai= de =9,- y = 5.5-2.8= 2.7 in I, = 7, + Adi 0.333 + 4 x 9.72 I = 29.493 in 4

for segment 2. pag ③ Tę - bd? - 24,2 dz 12 1-333 iny 12 A2 = 4 in 2 Y₂ - 4 - 2.8 = 1.2 in Iz+ Anda 1•333 + 4x (1.2)? 7.093 iny I, = Ig for segment 3. 3 Iz = bd? 4x3 ging 1 2 12 A2 = 12 in2 ds. j - Y3 2.8 -105 = 1.3 in 2 9 + 12 x 1.3 2x103 13 Iz + Azd} I3 = 2.9.28 iny Ina Ist I2 + I3 5 29.493 +7.093 + 29.28 I 65.866 iny we know that cola I ye 6- 2.8 y = 3.2 in Bending stress at Upper portion, 6 I 6 225 X 12 X 3.2 65.866 Bendin stress at lower portion. 6= my 131.175 lb inz Ans (max Bendin stress) y = 2.8 in 2 225 x 12 x 2.8 65.866 6 = 114.778 lb ina

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