1 A 250 mm x 125 mm I-beam having I, 3717-8 W V, y 30° U, x cm² and Iy = 193-4 cm4 is used as a purlin on a roof truss. The angle of inclina- tion of the beam rafter of the roof is 30° to the hori- zontal and the rafters are placed 4 m apart. If the vertical load on the purlin is 10 kN uniformly dis- tributed, determine the maximum stress and the maximum vertical deflec- tion of the purlin. Take the purlins to be simply sup- ported at the ends and E = 200 GPa. mpm 30° Fig. 9.16

1 A 250 mm x 125 mm I-beam having I, 3717-8 W V, y 30° U, x cm² and Iy = 193-4 cm4 is used as a purlin on a roof truss. The angle of inclina- tion of the beam rafter of the roof is 30° to the hori- zontal and the rafters are placed 4 m apart. If the vertical load on the purlin is 10 kN uniformly dis- tributed, determine the maximum stress and the maximum vertical deflec- tion of the purlin. Take the purlins to be simply sup- ported at the ends and E = 200 GPa. mpm 30° Fig. 9.16

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter6: Stresses In Beams (advanced Topics)

Section: Chapter Questions

Problem 6.5.10P: .10 A built-up bourn supporting a condominium balcony is made up of a structural T (one half of a W...

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.10 A built-up bourn supporting a condominium balcony is made up of a structural T (one half of a W 200 x 31.3) for the top flange and web and two angles (2 L 2 / b / 6.4. long legal back-lo-backl lot the bottom flange and web. as shown. The beam is subjected to a bending moment .1/ having its vector at an angle ft lo the z axis (see figure). Determine the or ion ta I ion of the neutral axis and calculate the maximum tensile stress ir, and maximum compressive stress tr. in ".he beam. .Assume that 9 = 30°andM = 15 kN · m. Use the numerical properties: c =4.111mm, c2 =4.169 mm, of = 134 mm, I, = 76 mm, A = 4144 mm 3 =3.88 X 106 mm 4, and = 34.18 X 10 mm 4.
.2 A ligmio.irc ii supported by two vorlical beams consistins: of thin-walled, tapered circular lubes (see ligure part at. for purposes of this analysis, each beam may be represented as a cantilever AB of length L = 8.0 m subjected to a lateral load P = 2.4 kN at the free end. The tubes have a constant thickness ; = 10.0 mm and average diameters dA = 90 mm and dB = 270 mm at ends A and B, re s pec lively. Because the thickness is small compared to the diameters, the moment of inerlia at any cross section may be obtained from the formula / = jrrf3;/8 (see Case 22, Appendix E); therefore, the section modulus mav be obtained from the formula S = trdhlA. (a) At what dislance A from the free end docs the maximum bending stress occur? What is the magnitude trllul of the maximum bending stress? What is the ratio of the maximum stress to the largest stress (b) Repeat part (a) if concentrated load P is applied upward at A and downward uniform load q {-x) = 2PIL is applied over the entire beam as shown in the figure part b What is the ratio of the maximum stress to the stress at the location of maximum moment?
Solve the preceding problem for a column with e = 0.20 in,, L = 12 ft, I = 2L7in4, and E = 30 × 106psi.
A small balcony constructed of wood issupported by three identical cantilever beams (seefigure). Each beam has length L1 = 2.1m, width b,and height h = 4b/3. The dimensions of the balconyfloor are L1 XL2, where L2 = 2.5 m. The designload is 5.5 kPa acting over the entire floor area.(This load accounts for all loads except the weightsof the cantilever beams, which have a weight densityΥ = 5.5 kN/m3.) The allowable bending stress in thecantilevers is 15 MPa.Assuming that the middle cantilever supports50% of the load and each outer cantilever supports25% of the load, determine the required dimensions band h.
A beam carries a uniform distributed load of intensity w in N/m. It was determined that Vmax = 7.5w N, (+)Mmax = 5.2w N-m, (-)Mmax = 4.5w N-m. From the given cross section shown, ytop = 64.183 mm, ybot = 135.817 mm, and INA = 25.059 x 10 6 mm4. The allowable stresses are as follows: σfT = 30 MPa, σfC = 60 MPa, and τ = 10 MPa. a. The safe uniform load considering tensile flexural strees is _____N/m b. The safe uniform load considering compressive flexural stress is _____ N/m. c. The moment inertia of the area about the neutral axis is _____ mm^3. d. The safe uniform load considering maximum shear force is _____ N/m e. Based on your analysis, the safe uniform load to recommend is _____ N/m.
A simply supported beam is subjected to alinearly varying distributed load q(x) =(x/L)q0 withmaximum intensity q0 at B. The beam has a lengthL = 4 m and rectangular cross section with a widthof 200 mm and height of 300 mm. Determine themaximum permissible value for the maximum intensity,q0, if the allowable normal stresses in tension andcompression are 120 MPa.
The horizontal beam is assumed to be rigid while supporting the distributed load. Determine the angle of inclination of the beam after the load is applied. Each support consists of a wooden post with a diameter of 120 mm and an original length (unloaded) of 1.40 m- Consider E = 12 GPa
A beam carries a uniform distributed load of intensity w in N/m. It was determined that Vmax = 3.75w N, (++)Mmax = 2.53w N-m, (−−)Mmax = 4.5w N-m. From the given cross section shown, ytop = 100mm, ybot = 150mm, and INA = 72.92 x 10 6 mm4. The allowable stresses are as follows: σfT = 40 MPa, σfC = 70 MPa, and τ = 10 MPa. (a) The safe uniform load considering tensile flexural stress is _____ N/m. (b) The safe uniform load considering compressive flexural stress is _____ N/m. (c) The moment of the area about the neutral axis is _____ mm3. (d) The safe uniform load considering maximum shear force is _____ N/m. (e) Based on your analysis, the safe uniform load to recommend is _____ N/m
In a 2.5 cantilevered I-beam, 2500 kg weight is applied at 0.75 meter from the free end. If the allowable stress in beam is 120 Mpa, determine the section modulus and The base and height of the beam if the base is 75% of its height mm.
A simply supported beam of span 3.0 m has a cross-section 120 mm × 180 mm. If the permissible stress in the material of the beam is 10 N/mm^2, determine maximum udl it can carry.
A beam is subjected to equal 19.1 kip-ft bending moments. Assume ty = t2 = ty= 1 in., d = 10 in, by= 4 in., and b2 = 7 in. The cross- sectional dimensions of the beam are illustrated. Determine; (a) the distance y to the centroid (measured from the bottom), the moment of inertia & about the z axis, and the controlling section modulus S, about the z axis. (b) the bending stress O, at point H (positive if tension, negative if compression). (c) the bending stress y at point K (positive if tension, negative if compression). (d) the maximum bending stress, Omax produced in the cross section (positive if tension, negative if compression).
A simply supported beam of span 3.0 m has a cross-section 120 mm × 180 mm. If the permissible stress in the material of the beam is 10N/mm2,determine(i)maximum udl it can carry (ii) maximum concentrated load at a point 1 m from support it cancarry. Neglect moment due to self weight.