C8-49 A 500-lb load is supported by a roller on a beam as shown in Fig. Plot |Mmax, the maximum bending moment in the beam, as a function of the roller position b (0 sbs 25 ft). -25 ft- A B 500 lb
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- A frame ABCD is constructed of steel wide-flange members (W8 x 21; E = 30 x ID6 psi) and subjected to triangularly distributed loads of maximum intensity q0acting along the vertical members (see figure). The distance between supports is L = 20 ft and the height of the frame is h = 4 ft. The members are rigidly connected at B and C. Calculate the intensity of load q0 required to produce a maximum bending moment of 80 kip-in. in the horizontal member BC. If the load q0 is reduced to one-half of the value calculated in part (a), what is the maximum bending moment in member BC? What is the ratio of this moment to the moment of 80 kip-in. in part (a)?The horizontal beam ABC of an oil-well pump has the cross section shown in the figure. If the vertical pumping force acting at end C is 9 kips and if the distance from the line of action ofthat force to point B is 16 ft, what is the maximum bending stress in the beam due to the pumping force?A heavy object of weight W is dropped onto the midpoint of a simple beam AB from a height h (see figure). Obtain a formula for the maximum bending stress ^ma* due to tne filing weight in terms of h, st, and 5st, where it is the maximum bending stress and Sstis the deflection at the midpoint when the weight W acts on the beam as a statically applied load. Plot a graph of the ratio o"max/ö"it (that is, the ratio of the dynamic stress to the static stress) versus the ratio iifS^r(Let h/S^ vary from 0 to 10.)
- Find an expression for required moment MA(in terms of q and L) that will result in rotation êB= 0 due to MAand q loadings applied at the same time. Also, what is the resulting net rotation at support A?A beam supporting a uniform load of intensity q throughout its length rests on pistons at points A, C and B (sec figure). The cylinders are filled with oil and are connected by a tube so that the oil pressure on each piston is the same. The pistons at A and B have diameter d1and the piston at C has diameter D2. (a) Determine the ratio of d2to d1so that the largest bending moment in the beam is as small as possible. Under these optimum conditions, what is the largest bending moment Mmaxin the beam? What is the difference in elevation between point C and the end supports?A rectangular beam with semicircular notches, as shown in part b of the figure, has dimensions h = 120 mm and h1= 100 mm. The maximum allowable bending stress in the plastic beam is emix = 6 M Pa, and the bending moment is M = 150 N · m. Determine the minimum permissible width bminof the beam.
- Find an expression for required moment MA(in terms of q and L) that will result in rotation 9B= 0 due to MAand q loadings applied at the same time. Also, what is the resulting net rotation at support A?Find required distance d (in terms of L) so that rotation Ss= 0 is due to M and q loadings applied at the same time. Also, what is the resulting net rotationA cant i levé r b ea m i s supported by a tie rod at B as shown. Both the tie rod and the beam are steel with E = 30 x 106 psi. The tie rod is just taut before the distributed load q = 200 lb/ft is applied. Find the tension force in the tie rod. Draw shear-force and bending-moment diagrams for the beam, labeling all critical ordinates.
- Divide the plane frame structure shown in the image into suitable parts for analytical examination and draw the free-body diagrams of the parts. Additionally, determine the shear force and bending moment diagrams of the structure. F = 10 kN and a = 2 m. There is a roller support on the left edge and a fixed support at the bottom.Determine the shear force, V and its bending moment, M. kindly provide the SFD and BMDA load of 100 kN, followed by another load of 50 kN, at a distance of 10 metres, advances across a girder with a 100-metre span. Obtain an expression for the maximum bending moment at a section of the girder at a distance of z metres from an abutment. Please provide solutions. Answer is z(140-1.5z) for z< (100/3)m;(100-z)(1.5z-5) for z>(100/3) m.