Problem 4: For the beam shown below, (a) using singularity function to determine equation of elastic curve of the beam, (b) find the deflection at C and the slope at A. Use E=29X106 psi A B 3 kips/ft C 20 kips -5 ft-5 ft-6 ft- D H W16 X 57
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- 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.)-5 Calen1ate the deflections S 3a ndA symmetric beam A BCD with overhangs at both ends supports a uniform load of intensity q (see figure). Determine the deflection SDat the end of the overhang. (Obtain the solution by using the modified form of Castiglianos theorem.)
- Beam ACE hangs from two springs, as shown in the figure. The springs have stiffnesses kxand k2and the beam has flex lira I rigidity EL (a) What is the downward displacement of point C, which is at the midpoint of the beam, when the moment M0 is applied? Data for the structure are as follows: M0= 10,0 kN m, L = 1.8 m, EI = 216 kN m2, Jt, = 250 kN/m, and k2= 160 kN/m, (b) Repeat part (a), but remove A/() and apply a uniform load q — 3.5 kN/m to the entire beam.A simple beam with an overhang is subjected to d point load P = 6kN. If the maximum allowable deflect ion at point C is 0.5 mm, select the lightest W360 section from Table F-l{b) that can be used for the beam. Assume that L = 3 m and ignore the distributed weight of the beam.For the beam and loading shown, use discontinuity functions to compute: (a) the deflection VA of the beam at A, and (b) the deflection Vmidspan of the beam at midspan (i.e., x = 2.45 m). Assume a constant value of El = 1270 kN-m² for the beam; M₁ = 9 kN-m, wo = 19.8 kN/m, LAB = 1.1 m, LBc = 2.7 m. MA A Answer: (a) VA = (b) Vmid i LAB i Wo B LBC mm. mm.
- A beam of uniform rectangular section 200 mm wide and 300 mm deep is simply supported at its ends. It carries a uniformly distributed load of 9 KN/m run over the entire span of 5 m. if the value of E for the beam material is 1 X 104 N/mm2 , find the slope at the supports and maximum deflection. Give me complete solution based on the given above. Again I need to ask the same question since you gave me a wrong answer before.beam, simply supported at its ends, carries a load which increases uniformly from 15kN/m at the left-hand end to 100 kN/m at the right-hand end. If the beam is 5m long, find the equation for the rate of loading and, using this, to determine the deflection of the beam at mid-span if E= 200GN/m² and I=600*10 m².The simply supported beam carries a uniformly distributed load over parts of its length. Compute (a) the midspan slope and deflection, (b) the slope and deflection at point C. Segment AC’s beam property is worth EI and segment BC’s beam property is worth 2EI. E = 200 GPa, I = 80x106 mm4. Solve problem using the Area Moment Method.
- For the beam and loading shown, use discontinuity functions to compute(a) the slope of the beam at C (positive if counterclockwise and negative if clockwise).(b) the deflection of the beam at C.Assume LAB = 210 mm, LBC = 140 mm, LCD = 120 mm, LDE = 260 mm, MB = 200 N-m, P = 1080 N and a constant value of EI = 590 × 106 N-mm2 for the beam.Calculate the beam deflection at point C. E = 206.8 GPa, I„ = 1.873 x 10-6 mª. Use either the double integration method or the moment area method. Show your work. 200 N 500 N 50.8 mm -------z 76.2 mm A 1 m 1 m 2 mThe simply supported beam consists of a W14 x 34 structural steel wide-flange shape [E = 29,000 ksi; 1= 340 in.4]. For the loading shown, use discontinuity functions to compute (a) the slope of the beam at E and (b) the deflection of the beam at C. Assume wo = 13 kips/ft, WcD = 6.0 kips/ft, LAB = 6.0 ft, LBc = 6.0 ft, LCD = 7.0 ft, LDE = 3 ft. Lus Part 1 Answer: By = i Wo B LAB + LBC kips Ey = i C WCD LCD D LDE Calculate the reaction forces at the supports. Upward forces are positive. E X