The beam AB shown in the figure supports a uniform load of intensity 3000 N/m acting all over half the length of the beam. The beam rests on a foundation that produces a uniformly distributed load W over the entire length. 3000 N/m w N/m 0.8 m 1.6 m 0.8 m
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- 1. *A propped cantilever has a 2m overhang. The beam has a load of 2W applied half way between the fixed support and the roller support and a load of W applied at the free end. What is the minimum value of W that will cause the beam to collapse? The beam has the cross-section shown below. The yield stress is 300 MPa. 75 mm 15 mm 300 mm 2W C D 15 mm 250 mm 15 mm, 2m B + 2m 2m(See figure) A 20 mm x 120 mm beam is subjected to a load of 50 KN acting at the centroid of the cross section as shown in the figure. Point B is 20 mm below the centerline of the beam. Figure 20 300 mm 120 20 man B 50 kN a. Find the shearing stress at point B. Ans: -16.67 MRa b. Find the minimım principal stress component on the 30 degrees plane at point B. Ans: 2.98 MPa2:37 6.00 KB/S A 2M 3M B Problem 2: A rigid block of negligible mass is supported by three symmetrically spaced rods as shown. Each copper rod has an area of 900mm2 and E=120GPA, and the allowable stress is 70MPa. The steel rod has an area of 1200mm2, E=200GPA and the allowable stress is 140MPA. Determine the largest load P which can be supported. Your answer Figure for Problem 2 STEEL 24OMM COPPER COPPER 16OMM 16OMM --
- SITUATION 32 The simply supported beam in the figure below has a rectangular cross section 120 mm wide and 200 mm high. a. Compute the maximum bending stress in the beam. a. Compute the bending stress at a point on section B that is 25 mm below the top of the beam. 0.8 m RA 6 kN/m B 2m NA с 120 mm 15 kN D A 100 mm -+ 100 mm 1.0 m E REA simply supported beam is subjected to a linearly varying distributed load q(x) = qo with maximum intensity 9, at B. The beam has a length L = 4 m and rectangular cross section with a width of 220 mm and height of 285 mm. %3D 90 9(x) Determine the maximum permissible value for the maximum intensity, go, (in kN/m) if the allowable normal stresses in tension and compression are 130 MPa. kN/mThe T section is shown in Figure below is the cross-section of a beam. The beam is subjected to a uniform distributed load = 4 kN/m. The N.A is located at 34.7 mm from the bottom and that IxA =10.64x106 mm. Determine (a) the maximum shearing suess (b) the shearing stress at 15 mm from the bottom face. Q2 %3D 20mm 4 kN/m 120mm A 34.7 mm 20mm lm 3m 1m 220mm TT
- The beam AC is assured to be rigid and is supported as shown. 2. If deflection at free end is 3 mm. What is the tensión in the rod? E = 200 GPa a. 35.58 kN c. 54.73 kN b. 68.49 kN d. 41.88 kN 3. What is the stress in the rod a. 133.33 MPa c. 154.73 MPa 4. If the stress in the rod is 200 MPa, b. 128.21 MPa d. 143.53 MPa what is the safest load W? a. 41.88 kN c. 54.37 kN b. 39.34 kN d. 48.64 kN ]3m@ 20mmo 2 mA steel girder of 6m length acting as a beam carries a uniformly distributed load w N/m run throughout its length. If I = 30 x 10-6 m* and depth 270 mm, calculate: (i) The magnitude of w so that the maximum stress developed in the beam section does not exceed 72 MN/m2. (ii) The slope and deflection (under this load) in the beam at a distance of 1.8 m from one end. Take : E = 200 GN/m2 %3D%3D QUESTION 2. An oblique bending moment of M = 5 kN.m is applied on the cross-section of an aluminum beam as shown in the figure. (a) Calculate the maximum values of compressive and tensile normal stresses on the crss section. (b) Define the orientation of the neutral axis and draw on the cross-sectionç. M = 5 kN.m 30° 10 mm 40 mm 10 mm A-40 mm--r: 30 mm 30 mm 10 mm 10 mm
- 1 Question 3: 2 The 60 mm diameter solid shaft is subjected to the distributed and concentrated torsional loadings 3 shown. Determine the absolute maximum and minimun shear stresses on the outer surface of the 4 shaft and specify their locations, measured from the fixed end A. Take: AA = 1.55 BB = 0.85 8. CC = 1205 kN / m 2 kN-m/m 9 10 11 AA m CC Nm 12 B. 13 вB m 14 15 16 Solution: 17 18 Te CC N.m 19 20 TAB 21 22 CC Nm Zooox N.m 23 24 25 26 CC N.m 27 28 The internal torque for segment BC is Constant T = cc NmHowever, 29 the internal for segment AB varies with x, 30 T- 2000 x+ AA = 0; T = (2000 x-cC) Nm 31 The minimum shear stress occurs when the internal torque is zero in segment AB. 32 By setting T = 0 33 0 = (2000 x -C; Ans 34 35 And 36 d = AA - x = Ans 37 Ans 38 39 The maximum shear stress occurs when the internal torque is the greatest. This 40 occurs at fixed support A where 41 d = Ans m 42 At this location, 43 (T . = 2000 AA-cc = 44 45 The polar moment of inertia of the rod is…The overhanging beam ABC in Figure supports a concentrated load and a uniformly distributed load. The beam has a rectangle cross-sectional area of 120 mm × 180 mm (base x height). Neglect the weight of the beam. a) Construct the shear-force and bending-moment diagram. b) Determine the maximum normal stress in the beam and its location measured from point A. Ans : omax 173.92 MPa 20 kN 12 kN/m A B 4 m 10 m 20A beam shown below has a T-shaped cross section. Determine the maximum compressive stress of the beam. T I = 87-49 in 4 400 16/+ ↓ ↓ ↓ ↓ ↓ ↓ ↓ B TOFT 16001b 160016 4.17 1° 3200 lbft 2.914 in - 3400/6 5.886 in -NA 4FT 10° 100016 -240016 -4000 16 ff 1000lb dc V M