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- calculate the location of the centroid, the second moments and product of area for the cross- section if; D = 67 mm, B = 41 mm & t = 2.41 mm A L Test beam A Strain gauge W (a) Unsymmetrical cantilever beam with weight applied at the free end and at the "shear centre", so that there is no torsion induced. Section A-A Strain gauge 1 Strain gauge 2 b Strain gauge 3 a B (b) Location of Huggenberger strain gauges From these, calculate the orientation and position of neutral axis for pure bending in the vertical plane (i.e. bending about a horizontal axis).A simply supported beam ABC is loaded at the end of a bracket BDE (see figure). D (Use the deformation sign convention. When entering expressions, use the following as necessary: P and L.) Draw the axial-force diagram for ABC. N N State expressions for the minimum and maximum values of the axial force Mx). Nain = max Draw the shear-force diagram for ABC. Vrur 00 State expressions for the minimum and maximum values of the shear force Vx). min V = max Draw the bending-moment diagram for ABC. M M OMeen O OMin State expressions for the minimum and maximum values of the bending moment M(x). Mmin = %3D 'maxThe moment acting on the cross section of the unequal-leg angle has a magnitude of 19 kN-m and is oriented as shown in the figure. All stresses are positive if tensile and negative if compressive. Assume a = 180 mm, b- 125 mm and t- 17 mm. Determine (a) the bending stress at point H. (b) the bending stress at point K. (c) the maximum tension and the maximum compression bending stresses in the cross section. (d) the orientation B of the neutral axis relative to the +z axis. b. y K H. (typ.) Answers: (a) OH = i MPa (b) OK = MPа (c) OmaxT = MPa OmaxC = MPa (d) B = i
- Determine the reactions at the supports, then draw the shear and moment diagram. Assume A is pin and B and C are rollers in the figure . El is Constant. Use only Method of Constant deformation or the so called Force Method. A. DEGREE OF INDETERMINANCY, NO OF REDUNDANT SUPPORT B. FBD DIAGRAM WITH CUTTING SECTIONS C. SOLUTIONS AND VALUE OF REACTIONS D. E. SHEAR AND MOMENT DIAGRAM 600 lb/ft A [B 15 ft 15 ftThe simple beam AB supports two connected wheel loads Pand 2P that are a distance d apart (see figure). The wheels may be placed at any distance z from the left-hand support of the beam. (Assume P = 8 kN, d = 2.6 m, and L = 22 m.) 2P A (a) Determine the distance z that will produce the maximum shear force in the beam. Round to two decimal places. m (b) Determine the maximum shear force Vmax - Round to two decimal places. kN (C) Determine the distance z that will produce the maximum bending moment in the beam, and also draw the corresponding bending-moment diagram. Round to two decimal places. m (d) Draw the corresponding bending-moment diagram. Maax =121.80 M (kN m) A. 8.83 m 60 m 10.57 m Млах 3109.62 M (kN m) В. 11.43 m 2.60 m 8.83 mThe right angle bar is supported by a pin at B and a roller at C as shown in figure. The 30 mm diameter pin is in double shear. The shear stress in the pin is limited to 120 MPa. Neglect torsional effect. 400 mm BC The maximum safe value of Pis 30° P 480 mm kN. (Round off to one decimal place)
- SITUATION. The tower for a transmission line is modeled by the truss shown. The crossed members in the center section of the truss may be assumed to be capable of supporting tension only. Given: P=2.8kN 0=15⁰ a=3m b=3m c= 5m 5 panels@(a)m each F E b G B b b C a Q Zoom image Compute the force on member CL PWeek 5, Question 2: Using the force method, calculate the bending moment at B for the statically indeterminate frame below. Please ignore the axial and shear deformations. Take a 12 kN and L = 5.5 m. a B EI A 2EI -3 m Calculate the bending moment at B: kN m MB 2EI m D EI E +=+ LTwo 160 mm * t cover plates are welded to two cahnnels 200 mm high to form the cross section of the beam shown in the figure. The moment of inertia of each channel about a horizontal axis through the centroid is 2.06*106mm4. a)Determine the support reactions. b)Draw the shear force and bending moment diagrams. c)If the allowable bending stress of the beam is 255 MPa, find the required thickness t of the plates to safely support the load.
- Rigid AD rod in the figure, at points A and C with two vertical elastic bars articulated at the ends vertical from point D to P intensity while standing horizontal the force is affected. Elongation stiffness of ela stic bars EA and their length is L. According to this, a) The forcesthat will occurin the elastic bars, b) the displacement of the D point of the rigid bar, c) Calculate the support reaction at point B. EA,L A B D. EA.L rijit Fa + a 2a-Determine the reactions at the support at A and B using Method of Consistent Deformation. (Please include the full solution of computing for the deflection using the Virtual Load Method)Two d mm*10 mm cover plates are welded to two UPN 200 channels 100 mm high to form the cross section of the compound beam shown in the figure. The moment of inertia of each channel about a horizontal axis through the centroid is 19.10*106 mm4. a) Determine the support reactions. b) Draw the shear force and bending moment diagrams. c) If the allowable bending stress of the beam is 300 MPa, find the required width d of the plates to safely support the load.