This is a challenging one! 10 kN 9 kN 10 kN m A B C D 1.5 m 1.5 m 1.5 m 1.5 m 1.5 m 1.5 m Compute the support reactions at A, C and E? [MA = 21.5kNm, A, = 2.67KN, C, = 16.67KN, E, = 5kN] А Hint: Isolate DE, then move to BD and so on.
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- Repeat the previous problem using sx= 12 MPa..17 A mountain-bike rider going uphill applies torque T = Fd(F = l5lb, d = 4 in.) to the end of the handlebars ABCD by pulling on the handlebar extenders DE. Consider the right half of the handlebar assembly only (assume the bars are fixed at the fork at A). Segments AB and CD are prismatic with lengths L, = 2 in.andL3 = 8.5 in, and with outer diameters and thicknesses d01 = 1.25 in. 101 = 0.125 in. and d03 = O.87in.,i03 = 0.ll5in, respectively as shown. Segment BC’ of length L, = 1.2 in. however. is tapered, and outer diameter and thickness vary linearly between dimensions at B and C. Consider torsion effects only. Assume G = 4000 ksi is constant. Derive an integral expression for the angle of twist of half of the handlebar tube when it is subjected to torque T = Fd acting at the end. Evaluate ‘b1-, for the given numerical1ues.Two sections of steel drill pipe, joined by bolted flange plates at Ä are being tested to assess the adequacy of both the pipes. In the test, the pipe structure is fixed at A, a concentrated torque of 500 kN - m is applied at x = 0.5 m, and uniformly distributed torque intensity t1= 250 kN m/m is applied on pipe BC. Both pipes have the same inner diameter = 200 mm. Pipe AB has thickness tAB=15 mm, while pipe BC has thickness TBC= 12 mm. Find the maximum shear stress and maximum twist of the pipe and their locations along the pipe. Assume G = 75 GPa.
- A plane frame with a pin support at A and roller supports at C and £ has a cable attached at E. which runs over Frictionless pulleys al D and B (see figure). The cable force is known to be 400 N. There is a pin connection just Lo the left of joint C. (a) Find reactions at supports^, C, and E. (b) Find internal stress, resultants N, V, and M just to the right of joint C. (c) Find resultant force in the pin near C.: A hollow, pressurized sphere having a radius r = 4.8 in, and wall thickness t = 0.4 in. is lowered into a lake (see figure). The compressed air in the tank is at a pressure of 24 psi (gage pressure when the tank: is out of the water). At what depth D0will the wall of the tank be subjected to a compressive stress of 90 psi?A non prism elk- bar ABC made up of segments AB(length £,, cross-sectional area .Inland BC (length i-,, cross-sectional area A2) is fixed at end A and free al end C (see figure). The modulus of elasticity of the bar is E. A small gap of d intension s exists between the end of the bar and an elastic spring of length Lj and spring constant k3. If bar ABC only (not tin? spring} is subjected to temperature increase A3", determine the following. (a) Write an expression for reaction forces R^ and RDif the elongation of /I BC exceeds gap length s. (b) Find expressions for the displacements of points B and C if the elongation of ABC exceeds gap length s.
- A hollow circular pipe (see figure} support s a load P that is uniformly distributed around a cap plate at the top of the lower pipe. The inner and outer diameters of the upper and lower parts of the pipe are d1= 50 mm, d2= 60 mm, rf3 = 57 mm, and d1= 64 mm, respectively. Pipe lengths are Lt= 2 m and L, = 3 m. Neglect the self-weight of the pipes. Assume that cap plate thickness is small compared to I, and E,. Let E = 110 MPa. (a) If the tensile stress in the upper part is d = 10.5 MPa. what is load PI Also, what are reactions ft, at the upper support and R-, at the lower support? What is the stress ar(MPa) in the lower part? (b) Find displacement S(mm) at the cap plate. Plot the axial force diagram (AFD) [Ar(.f)] and axial displacement diagram (ADD)[5(.t)]. (c) Add the uniformly distributed load q along the censorial axis of pipe segment 2. Find q (kN/m) so that It, = 0. Assume that load P from part (a) is also applied.Solve the preceding problem if the mass of the tailgate is MT— 11 kg and that of the crate is hic— 6S kg. Use dimensions H = 305 mm, L = 406 mm, dc= 460 mm, and dT= 350 mm. The cable cross-sectional area is At= 11.0 mm'. (a) Find the tensile Force T and normal stress T in each cable. (b) IF each cable elongatesSolve the preceding problem (W 250 × 44.8) if the resultant force P equals 110 kN and E = 200 GPa.
- A steel riser pipe hangs from a drill rig located offshore in deep water (see figure). (a) What is the greatest length (meters) it can have without breaking if the pipe is suspended in the air and the ultimate strength (or breaking strength) is 550 MPa? (b) If the same riser pipe hangs from a drill rig at sea, what is the greatest length? (Obtain the weight densities of steel and sea water from Table M, Appendix I. Neglect the effect of buoyant foam casings on the pipe.)Space frame A BCD is clamped at A, except it is Free to translate in the .v direction. There is also a roller support at D, which is normal to line CDE. A triangularly distributed Force with peak intensity q0 = 75 N/m acts along AB in the positive - direction. Forces Px= 60 N and Pz = = 45 N are applied at joint C, and a concentrated moment My = 120 N . m acts at the mid-span of member BC. (a) Find reactions at supports A and I). (b) Find internal stress resultants N. E’I T, and .11 at the mid-height of segment AB.III. A circular steel rod has a diameter of 50 mm. It touches the unyielding supports at point A and B when T1 = 80 °C. Find the applied force P to the collar at its midsection so that, when T, = 30 °C, the reaction at B is zero. Use E st = 200 GPa and the coefficient of linear expansion of steel is at 12 x 10^-6 m/m C. |A B P. -0.5 m- 0.5 m Solve for the following: a) Thermal deformation in steel, St (st) b) Axial deformation of steel, Sp = c) Applied force in the collar, P = %3D mm (in terms of P, kN