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A beam subjected to axial loading will experience an axial stress, σa. If in addition, the beam is subjected to a bending load, a bending stress, σb, will also occur at the outer fibers of the beam. The maximum stress at the outer fibers of the beam will be σmax = σa + σb. Assume that σa and σb are independent and
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Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
- A shaft is made of a polymer having an elliptical cross section. If it resists an internal moment of M = 50 N # m, determine the maximum bending stress in the material (a) using the flexure formula, where Iz = 1 4 p(0.08 m)(0.04 m)3, (b) using integration. Sketch a three-dimensional view of the stress distribution acting over the cross-sectional area. Here Ix = 1 4 p(0.08 m)(0.04 m)3.arrow_forwardTwo elastic beams with equal bending rigidity of EI are connected by a pin at B. The beam is fixed at A and a roller support is attached at C. Beam BC is subjected to a uniformly distributed load of magnitude w=1 N/m. If the bending rigidity EI is 108Nmm2, determine a) the lateral deflection at B, b) the rotational angle at B, c) the rotational angle at C. d) sketch the deformed shapearrow_forward1. A thin high-strength steel plate having a thickness of 40 mm has a height of 120 mm and length of 350 mm, is subjected to a moment at both ends = 66 kN.m. E = 28000 MPa Determine the bending stress of the steel plate in MPa a. 1440 b. 1855 c. 1344 d. 2063 e. 2333 Determine its radius of curvature in mm. a. 272 b. 558 c. 154 d. 434 e. 166 2. According the NSCP 2015, the first hoop for beams and girders shall be located not more than 50 mm from the face of the supporting columns. The maximum spacing of hoops shall not exceed... a. 150mm b. d/4 c 6 times bar diameter d. all of the above 3. Based on NSCP 2015 Seismic requirement on concrete girders (beams with special moment frames, which of the following most nearly gives the required width (bw) of beam if its overall height is 600 mm. a. 250mm b. 180mm c. 300mm d. 350mm e. 400mm PLEASE ANSWER ALLarrow_forward
- a) 1. The support reaction forces at the A and C, in terms of P,be careful of the sign. 2. Give the expressions of the shear and moment at an arbitrary poistion x of AB segment, in terms of P and x, be careful of the sign. 3. Give the expressions of the shear and moment at an arbitrary poistion x of BC segment, in terms of P and x, be careful of the sign. b)Given l= 1000 mm, P= 4000 N and l1/l=0.66, calculate the internal shear force and draw the moment diagramarrow_forwardA beam has a bending moment of 3.5 kN-m applied to a section with a hollow circular cross-section of external diameter 3 cm and internal diameter 2.3 cm . The modulus of elasticity for the material is 210 x 109 N/m2. Calculate the radius of curvature and maximum bending stress. Also, calculate the stress at the point at 0.6 cm from the neutral axis (i) The moment of inertia in (mm^4)= ii) The radius of curvature in (mm) = (iii) The maximum bending stress in (N/mm^2)= iv) The bending stress at the point 0.6 cm from the neutral axis in (N/mm^2)=arrow_forwardAnswer p1 and Part 2: Determine the shear force acting at each of the following locations:(a) x = 11.0- ft (i.e., just to the left of point B)(b) x = 11.0+ ft (i.e., just to the right of point B)(c) x = 28.5 ftNote that x = 0 at support A. When entering your answers, use the shear-force sign convention detailed in Section 7.2.Answers: a) V = ____ kips b) V = ____ kips c) V = ____ kips Part 3: Determine the bending moment acting at each of the following locations:(a) x = 11.0 ft (i.e., at point B)(b) x = 28.5 ftNote that x = 0 at support A. When entering your answers, use the bending-moment sign convention detailed in Section 7.2. Answers: a) M = ____ kips-ft b) M = ____ kips-ft Part 4: Use your shear-force and bending-moment diagrams to determine the maximum bending moment, Mmax, and its location, xmax. Use the bending-moment sign convention detailed in Section 7.2.Answers: Mmax = ____ kips-ft xmax = ____ ftarrow_forward
- PART 1 answer Ay=45kN Dy=140kn PART 2 Determine the shear force acting at each of the following locations: (a) x = 2m (b) x = 6m (c) x = 9m (d) x = 12m My Answer: (a) V= 45kN (b) V= -20kN (c) V= -110kN (d) V= 30kN PART 3 Determine the bending moment acting at each of the following locations: (a) x=4m (b) x = 8 m (c) x = 10 m When entering your answers, use the bending moment sign convention. Need Answers: (a) M= ________________kN-m (b) M= ________________kN-m (c) M= ________________kN-marrow_forwardIn determining the bending stress, what conclusion can be drawn if the neutral axis is an axis of symmetric of the cross-section? a. The maximum tensile and compression bending stresses are equal in magnitude and occur at the section of the largest bending moment. b. The maximum tensile and compression bending stresses are equal in magnitude and occur at the section of the smallest bending moment. c. None of the choices d. The maximum tensile and compressive bending stresses may occur in different sections.arrow_forwardA steel bar of 0.8 x 2.5-in. rectangular cross section is subjected to two equal and opposite couples acting in the vertical plane of symmetry of the bar (Fig. . Determine the value of the bending moment M that causes the bar to yield. Assume σY= 36 ksiarrow_forward
- The beam shown has the following data:w1 = 10.0 kN/mw2 = 30.4 kN/mx = 14.8 my = 4.8 mDetermine the magnitude of the reaction force at C in kNarrow_forward34. The maximum tensile stress developed in a rectangular beam loaded transversely downward occurs at: A. Extreme top fiber B. Extreme bottom fiber C. Neutral Axis D. Anywhere in the sectionarrow_forwardDetermine the shear force acting at each of the following locations:(a) x = 0+ ft (i.e., just to the right of support A)(b) x = 9 ft(c) x = 12.333333333333 ftWhen entering your answers, use the shear force sign convention.Answer:(a) V = kips.(b) V = kips.(c) V = kips. The shear-force diagram crosses the V = 0 axis between points A and B. Determine the location x where V = 0 kips.Answer: x = Enter your answer in accordance to the question statement ft. Determine the maximum bending moment that acts anywhere in the beam. When entering your answer, use the bending moment sign convention.Answer: Mmax = Enter your answer in accordance to the question statement kip-ft. Use the graphical method to determine the bending moment acting at each of the following locations:(a) x = 3.3 ft(b) x = 9 ft(c) x = 12.6 ftWhen entering your answers, use the bending moment sign convention.Answers:(a) M = kip-ft.(b) M = kip-ft.(c) M = kip-ft.arrow_forward
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