For the beam shown: Find the maximum possible principal stresses at points C and D on the cross section shown. Data are as follows: P= 6.2 kN, L= 3.2 m, d = 1.25 m, b = 80 mm, t= 25 mm, h = 120 mm, and h, = 90 mm. h B
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- The Z-section of Example D-7 is subjected to M = 5 kN · m, as shown. Determine the orientation of the neutral axis and calculate the maximum tensile stress c1and maximum compressive stress ocin the beam. Use the following numerical data: height; = 200 mm, width ft = 90 mm, constant thickness a = 15 mm, and B = 19.2e. Use = 32.6 × 106 mm4 and I2= 2.4 × 10e mm4 from Example D-7A canti lever beam A B of a n isosceles t rapezoi-dal cross section has a length L = 0.8 m, dimensions bx= 80 mm and b2= 90 mm, and height h = 110 mm (see figure). The beam is made of brass weighing 85 kN/m3. Determine the maximum tensile stress asand maximum compressive stressSolve the preceding problem for a box beam with dimensions h = 0.5 m, h = 0.18 m, and t = 22 mm. The yield stress of the steel is 210 MPa.
- A W 200 x 41.7 wide-flange beam (see Table F-l(b), Appendix F) is simply supported with a span length of 2.5 m (see figure). The beam supports a concentrated load of 100 kN at 0.9 m from support B. At a cross section located 0,7 m from the left-hand support, determine the principal stresses tr, and 2and the maximum shear stress rnMJt at each of the following locations: (a) the top of the beam, (b) the top of the web, and (c) the neutral axis,An aluminum pole for a street light weighs 4600 N and supports an arm that weighs 660 N (see figure). The center of gravity of the arm is 1.2 m from the axis of the pole, A wind force of 300 N also acts in the (y) direction at 9 m above the base. The outside diameter of the pole (at its base) is 225 mm, and its thickness is 18 mm. Determine the maximum tensile and compressive stresses o, and e1., respectively, in the pole (at its base) due to the weights and the wind force.A simply supported wide-flange beam of span length L carries a vertical concentrated load P acting through the centroid Cat the midpoint of the span (see figure). The beam is attached to supports inclined at an angle « to the horizontal. Determine the orientation of the neutral axis and calculate the maximum stresses at the outside corners of the cross section (points A, B. ZX and E) due to the load P. Data for the beam are W 250 x 44,8 section, L = 3.5 m, P = 18 kN, and a = 26,57 Note: See Table F-l(b) of Appendix F for the dimensions and properties of the beam.
- A cantilever wood beam with a width b = 100 mm and depth h = 150 mm has a length L = 2 m and is subjected to point load P at mid-span and uniform load q = 15 N/m. (a) If the normal stress trx= 0 at point C, located 120 mm below the top of the beam at the fixed support A, calculate the point load P, Also show the complete state of plane stress on the element at point C (b) Repeat Part a if er = 220 kPa. Assume that element C is a sufficient distance from support A so that stress concentration effects are negligible.A circular post, a rectangular post, and a post of cruciform cross section are each compressed by loads that produce a resultant force P acting at the edge of the cross section (see figure). The diameter of the circular post and the depths of the rectangular and cruciform posts are the same. For what width b of the rectangular post will the maximum tensile stresses be the same in the circular and rectangular posts? Repeat part (a) for the post with cruciform cross section. Under the conditions described in parts (a) and (b), which post has the largest compressive stress?For a steel circular cantilever beam, 10mm in diameter, 700mm in length with an applied load of 7.848N in the free end, produce a sketch showing the distribution of stresses across the beam section for an applied moment of M=(3/4My+1/3Mp). Where My=24543.5 N.mm and Mp=41666.66667 N.mm and yeild stregth of material is 250Mpa. Cheers
- Two vertical forces are applied to a simply supported beam, having the cross section shown. Assume LAB=LCD=1.6 m, LBc=5.6 m, P=20 kN, b-205 mm, t-12 mm, tw-8 mm, d=177 mm. Determine the maximum tension (a positive number) and compression (a negative number) bending stresses produced in segment BC of the beam. Answers: OmaxT = Omaxc = LAB IN P B LBC bf T | ktw Cross section MPa MPa P LCD d D XA cantilevered beam of rectangular section (b width=3 inches ), h camber=12 inches ) is subjected to a concentrated load P=17 lb at the free downward end. Calculate the principal stresses and their directions, as well as the maximum shear stress at point "A". Point A is located at a distance c=2.5 ft from the free end and at a distance d=3 inches from the top of the beam. Show diagrams related to the solution of your problem.Two vertical forces are applied to a simply supported beam, having the cross section shown. Assume LAB=LCD=1.6 m, LBc=5.6 m, P=20 kN, b-205 mm, t-12 mm, tw-8 mm, d=177 mm. Determine the maximum tension (a positive number) and compression (a negative number) bending stresses produced in segment BC of the beam. Answers: OmaxT = omaxc = LAB MO P B 1339.48 i 329 LBC bf Cross section MPa MPa P LCD d D X