A W610 x 155 wide flange beam of length L = 4 m is suspended by two cables as shown. The unit mass of the beam is 155 kg/m. For 0= 40 deg, the tension in each cable is best given by a. 9.46 kN b. 4.73 kN c. 3.97 kN d. 0.482 kN 0 L/2 01 L/2
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- Solve the preceding problem for a column with e = 0.20 in,, L = 12 ft, I = 2L7in4, and E = 30 × 106psi.A sandwich beam having steel faces enclosing a plastic core is subjected to a bending moment M = 5 kN · m. The thickness of each steel face is 1 = 3 mm with modulus of elasticity E = 200 GPa, The height of the plastic core is hp= 140 mm, and its modulus of elasticity is Ep= 800 MPa. The overall dimensions of the beam are h = 146 mm and h = 175 mm. Using the transformed-section method, determine the maximum tensile and compressive stresses in the faces and the core.An S6 × 12.5 steel cantilever beam AB is supported by a steel tic rod at B as shown. The tie rod is just taut when a roller support is added at Cat a distance s to the left of £, then the distributed load q is applied to beam segment AC, Assume E = 30 × 106 psi and neglect the self-weight of the beam and tie rod. Sec Table F-2(a) in Appendix F for the properties of the S-shape beam. (a) What value of uniform load q will, if exceeded, result in buckling of the tie rod if L1, =6 ft, s = 2 ft, H = 3 ft, and d = 0.25 in.? (b) What minimum beam moment of inertia ibis required to prevent buckling of the tie rod if q = 200 lb/ft, L1, = 6 ft, H = 3 ft, d = 0.25 in., and s = 2 ft? (c) For what distance s will the tic rod be just on the verge of buckling if q = 200 lb/ft, L1= 6 ft, M = 3 ft, and d = 0.25 in.?
- A beam of 8m length rests on two supports one at the right end and the other 2m from the left end. The beam carries a udl of 15kN/m over the entire span and a concentrated load of 80kN at the middle of its span. Draw SFD and BMD . Mark all salient values and locate point of contra-flexure. Ans: RB = 120kN, MC = 172.5kNm, x1 = 0.343m from B. answer must tally with those givena machine mass m = 500 kg is mounted on a simply supported steel beam of length l = 2 that has a rectangular cross section (thickness = 0.1 m and width 1.2 m) and whose young modulus is given by E = 2.06x10 ^ 11 N / m2. To reduce the vertical deflection of the beam, a spring of stiffness k is added in the middle of the span, as shown in the following figure. Determine the value of k necessary to reduce the deflection of the beam by: a) -25% of its original valueb) -50% of its original valuec) -75% of its original valuePRIOR ANSWERS: Reaction Forces: By = 76.809 Cy = 15.94 Shear Forces: V (× = 10.5- ft (i.e., just to the left of support B)) = -36.75 kips V ( x = 10.5+ ft (i.e., just to the right of support B)) = 40.059 kips V (x = 25.5 ft) = -12.441 kips V (x = 26.5- ft (i.e.. just to the left of support C))= = -15.941 kips Bending moment: M (x = 10.5 ft (i.e., at support B)) = -192.9375 kips-ft M (x = 25.5 ft) = 14.1975 kips-ft
- 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 shallow foundation supported by a silty sand is shown in Figure 7.5. Given:Length: L = 2 mWidth: B = 1 mDepth of foundation: Df = 1 mThickness of foundation: t = 0.23 mLoad per unit area: qo = 190 kN/m2Ef = 15 x 106 kN/m2The silty sand has the following properties:H = 2 mμs = 0.4Eo = 9000 kN/m2k = 500 kN/m2/mUsing Eq. (7.17), estimate the elastic settlement of the foundation.A 70kg human steps at the tip of a springboard used to dive in a pool. The springboard has a length of 1.75 meters, moment of inertia is 0.000002 m^4, and modulus of elasticity is 150 GPa. Determine the deflection of the springboard in millimeters. Note: δ=[(W)(L^3)]/[(3)(E)(I)] for a cantilever beam with end force.
- Given the following properties of bridge deck girder: Barrier Weight, BW = 7.3kN/m Future wearing surface load = 1.20 kPa, Span length, L=12.0 m, Load of stay-in-place metal forms, wsmf=0.335kPa Unit wt of concrete, wc=23.54 kN/m³ Slab thickness = 200mm. •Determine the shear and moment per interior girder due to Dead Load, DC. •Determine the shear and moment per interior girder due to Dead Load, DW.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.The cantilever is subjected to a point force "P" in the middle of the beam span. The beam's modulus of elasticity, E-200 GPa and moment of inertia, l= 6x10^6 mm^4, are the same at every point. Accordingly, in which option is the maximum deflection (vertical displacement) in the beam given in "mm"? P= 12 kN, L= 2.8 m.