Part 2: Suppose, a vertical roller support is added at point C. Use only Area-Moment method. 1. Determine the degree of indeterminacy of the system. 2. Determine the Reaction force at C (in kN). 3. Determine the reaction force at A (in KN).
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- a beam is supported by a pin support at A and a roller support at B. For this question, leave your answer in terms of the variables w and L. (a) Using equilibrium of the full beam, find the support forces at A and B. (b) First section: Make an arbitrary cut between points A and B. Take the distance of the cut to be x along the beam from point A. Draw the free-body diagram for the left section and find functions for the internal shear force, V(x), and bending moment, M(x), in the section of the beam between A and B. (c) Second section: Repeat part (b) for the section of the beam between B and C. Take x to still be the distance from point A. (f) Find the value of x at which V(x) = 0. The internal bending moment reaches a maximum at the same point as V(x) = 0. Find the maximum bending mo- ment. pin Sketch the shear and bending moment diagrams. B L W C roller7. A compound lever as shown below. Find the effort P. if the system is used to lift a mass of 800kg. (10) S00 mam 400 mm 350 mm S0mm 800 kg 8. An oil drum 600mm in diameter and length Im is to be rolled over a step 120mm in height. Find the least pull through the centre of the drum required just to turn the drum over the step. Also find the reaction on the step. Assuming all the surfaces to be smooth. Take density of oil as 1 kg/litre and neglecting weight of the drum. (10) 50 mmA cantilever beam is free of support at point A and is clamped at the point B, as showr in the Figure Q4 below. Calculate the support reaction force and moment for the non- uniformly distributed load, where w = 64 N/m and L =6 m. The downward directior is denoted as positive direction in force and the anti-clockwise direction is defined as positve in moment. For all numerical answers, answer to within 3 decimal places. w A B. y Figure Q4: A cantilever beam under non-uniformly distributed load (a) The support reaction force at point B, be careful of the sign. R = (N) (b) The support reaction moment at point B, be careful of the sign. (N*m)
- Problem 3: A bent beam ABCD is held in equilibrium by a roller at A and by a pinned connection at D. The beam supports a uniform distributed load (80 lb/ft) over section AB and a concentrated force (390 lb) at point C. The roller at A rests against an inclined surface that is oriented 30° from the horizontal direction. Neglect the weight and depth of the beam and the size of the roller in this analysis. (a) Draw a complete FBD of beam ABCD. Clearly label all loads, reactions, and distances. (b) Determine all reactions at A and D. 80 lb/ft 30°/ 8 ft B 4 ft D 390 lb 12/12 3 ftmb: L d- ms A horizontal L=1.2 m long mb=12 kg uniform bar is hinged on the left end and pulled at the right end by a cable. The cable makes 31° angle with horizontal. A 18 kg store sign is suspended below the bar at d=0.18 m from the right end. Find the magnitude of vertical hinge force.Q2: A simply supported beam AB has a length of 3 m and carries distributed load which varies in linear manner from (1w) N/m at A support to (2w) N/m at the B support and concentrated load (1.5w) N at 2 m from A support, and the beam has hollow circular cross section of diameter ratio din/dout =1/3. Draw S.F. and B.M. diagrams for the beam and determine the value of (w) if the maximum bending stress 110 N/mm?, and the average shear stress at 1 m from point A equal to 15 N/mm?.
- Q2: A simply supported beam AB has a length of 3 m and carries distributed load which varies in linear manner from (1w) N/m at A support to (2w) N/m at the B support and concentrated load (1.5w) N at 2 m from A support, and the beam has hollow circular cross section of diameter ratio din/dout =1/3. Draw S.F. and B.M. diagrams for the beam and determine the value of (w) if the maximum bending stress 110 N/mm2, and the average shear stress at 1 m from point A equal to 15 N/mm?.Q2: A simply supported beam AB has a length of 3 m and carries distributed load which varies in linear manner from (1w) N/m at A support to (2w) N/m at the B support and concentrated load (1.5w) N at 2 m from A support, and the beam has hollow circular cross section of diameter ratio din/dout =1/3. Draw S.F. and B.M. diagrams for the beam and determine the value of (w) if the maximum bending stress 110 N/mm2, and the average shear stress at 1 m from point A equal to 15 N/mm2.Original problem: Set up equations needed to determine moments acting at joints as function of flexural rigidity using Force Method. Joint A - fixed support Joint B- rocker Joint C- pin (hint: pin at the end of the beam) 10 kN/m 9 m 6 m. MAn= MBA= Mac= Moment equilibrium equation at B:
- 3. Find all the support reactions A and N and also calculate all the internal forces in the truss and state whether in tension or compression. Use either the method of joints or sections. Consider JY = YN = NJ, LO = ON = NL = JP = PL = %3D %3D LJ = GQ = QJ = JG and OL // JY //GX. U V W X Y T S R Р Ac В с D F G H J N M K 100 kN 100 kNFor problem on the picture. assume that the left side of the spring has a fixed end and the other side has pull force applied to it. The force applied to the spring is 3lbf. Solve for the following:a. Draw the free body diagram using the equivalent spring constantb. total deformation of the springA statically determinate three-hinged arch is shown below, L = 1.5 m and P = 3 kN. Compute the support reactions and internal forces at Sections C™ and Cº. (All reaction force and internal force answers to be entered as absolute values.) a) A Thim 2P |L6-L O B O RDy= b) C Analyse the whole arch to determine the vertical reaction forces: RA, = RDX = P 1 O KN KN 6 m 6 m Analyse either freebody AC or CD to determine the horizontal reaction forces: RAx= (T) kN D kN Thim c) Use freebody AC to determine the following: (note that subscript CL represents left of C, i.e., C) Internal axial force NCL = KN