Question

[Quiz#03]: 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. [12 marks] b) For the given cross section for member ABC determine the centroid and the moment of inertia (1) with respect to Neutral Axis. [12 marks] c) If the maximum bending moment is 225 lb-ft, determine the maximum absolute bending stress and its location along the member ABC. [6 marks] P = 150 lb I 1.5 ft 1.5 ft 11 in 2 in 1 in 6 in 3 in 4 in

Answer 1

Sols (a) FBD оо the system is :- 1 Р: 150 B HA Using Statices, we get 2F=0 , НА+ Ир о (і) & fy=0 ; NA - 150 = 0 Хило, их 1:S + 150X3 = 0 ио 2 с - Зоо Ль ИА - Зоо ХЬ VA= 150 lb. Drauring the FBD of ABC, we get Р= 150 Jь HA usº foo

Nowo, ИА FBO osus = 20 2 FBo7 чач, авч дЬ Зоо ць 10 ХЬ Зььь B 1:s sft Зооль 1sg. 1 ДЬ Section AB - (044 $ 1:s 4-) Sxx = 150 ДЬ Зоо Б A Sk- SA = - 150 Ль, 10 % Х 19ь Mxxa 150 x МА- 0 Иe - 225 lb.ft Section BL :- Cosas 1. Sfo 34. – 1So XЬ х 1ъ ЛЬ SB= 150 lb S = 150 lb - 2 А - 150 х – даЅ A - Я, Me=0

3ook 4So 16 3 Зоо Јь 2 с. Зоо Іь 150 il 4sъдь 150 % (+) А SFD с. -) 1SD 15. ДЬ в А. с +) Вир 225 lb-ft (b) Is in 2 бі, () (я 3 т

Section (%) 4 Area (A) lin) 1 3x43 12 1S 2 2 - ч ч 3 чX1 - Ч 5,5 ч - А. Я. 1 А, A343 А, t A, + Аз ý = (1ax 1-s) + (ч.ч) + ( 41 SS) 12 тч +4 اری , 8 м Moment of Inertia :- + (3хч) х (а+8 - 1:s I xx 19 4х4(3? - 12 24 . a8 Ч Т$*4 = Lх (2) + (212)к (ч. 2-85- Тъ, 1а 1. 0933 Ч Тхъ, 4,4% (1 + (411) 1( 5-s- : 85- Ex3 = 12 24. 49 33 % Т%3 -

Ixx= Ixx at Ixx₂ + IXX3 5 Ixx = 29.28 + 7-0933 + 29.49 33 Ixyz 65.8666 in (c) Mmax= 225 lb ft M max = 1225 X 12 ) lb in Mmax 2700 lb. in Maximum 9 = (6-2.8)= 3.2 in 10613 Mmax y I 2700 X 3.2 65.8666 131. 144 psig Bending 131. 174 psi and its bestion as at top of ... Maximum Absolute Stress is I cross-section. Completed