Determine the reactions at pin A and rollers B and C of the continuous beam shown below.
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- A fixed-end beam AB supports a uniform load of intensity q = 75 lb/ft acting over part of the span. Assume that EI = 300kip-ft2. Calculate the reactions at A and B. Find the maximum displacement and its location. Repeat part (a) if the distributed load is applied from A to B.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.?An aluminum bar having a rectangular cross section (2.0 in. × 1.0 in.) and length L = 30 in. is compressed by axial loads that have a resultant P = 2800 lb acting at the midpoint of the long side of the cross section (sec figure). Assuming that the modulus of elasticity E is equal to 10 × 106 psi and that the ends of the bar are pinned, calculate the maximum deflection and the maximum bending moment Mmax.
- Solve t he preceding problem by integrating the differential equation of the deflection curve.The equation of the deflection curve for a cantilever beam is v(x)=m0x22EI Describe the loading acting on the beam. Draw the moment diagram for the beam.‘11.5-2 A steel bar having a square cross section (50 mm × 50 mm)and length L = 2.0 in is compressed by axial loads that have a resultant P = 60 kN acting at the midpoint of one side of the cross section (sec figure). Assuming that the modulus of elasticity £is equal to 210 GPa and that the ends of the bar are pinned, calculate the maximum deflection S and the maximum bending moment Mmax.
- A fixed-end b earn is subjected to a point load at mid-span. The beam has a rectangular cross section (assume that the h/b ratio is 2) and is made of wood (E = 11GPa). Find height h of the cross section if the maximum displacement of the beam is 2 mm. Calculate the displacement of the beam at the inflection points.The frame A BC support s a concentrated load P at point C (see figure). Members AB and BC have lengths h and fh respectively. Determine the vertical deflection Scand angle of rotation $c at end C of the frame, (Obtain the solution by using the modified form of Ca s tig] i a no s theorem.)The deflection curve for a simple beam AB (sec figure) is given by v=q0L44EIsinxL Describe the load acting on the beam. Deter mine the reactions RAand RBat the supports, Determine the maximum bending moment Mmax.
- Use the method of superposition to find the angles of rotation 9Aand SBat the supports, and the maximum deflection for a simply supported beam subjected to symmetric loads P at distance a from each support. Assume that EI is constant, total beam length is L and a = U3. Hint: Use the formulas of Example 9-3.Given the Statically Determinate Simple Beam as shown below withinternal hinged at Point B and additional external support at Point D (0.9 m fromPoint A). 10N/mDetermine the following:a.) The External Reaction at Point A.b.) The Internal Reaction at Point B.c.) The External Reaction at Point C.d.) The External Reaction at Point D. express in 3 decimal pointsDetermine the values of the reactions in the cantilever beam