The cantilevered handle in the figure is made from mild steel that has been welded at the joints. The lengths are a = 7 in, b = 5 in, and c=1.5 in. For Fx = 0, Fy=175 lbf, and F₂ = 0. Use Castigliano's theorem to determine the vertical deflection (along the y-axis) at the tip. Note that when calculating the torsion strain energy of a noncircular cross section, Jis not the polar moment of inertia. Instead, use Eq. 3-41 to determine an equivalent Jeq for the solid rectangular cross section of member BC. y The vertical direction at the tip is , 1-in dia. B in in. 1/in b in dia.

The cantilevered handle in the figure is made from mild steel that has been welded at the joints. The lengths are a = 7 in, b = 5 in, and c=1.5 in. For Fx = 0, Fy=175 lbf, and F₂ = 0. Use Castigliano's theorem to determine the vertical deflection (along the y-axis) at the tip. Note that when calculating the torsion strain energy of a noncircular cross section, Jis not the polar moment of inertia. Instead, use Eq. 3-41 to determine an equivalent Jeq for the solid rectangular cross section of member BC. y The vertical direction at the tip is , 1-in dia. B in in. 1/in b in dia.

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter1: Tension, Compression, And Shear

Section: Chapter Questions

Problem 1.9.7P: A steel riser pipe hangs from a drill rig. Individual segments of equal length L = 50 ft are joined...

See similar textbooks

Similar questions

A hollow circular tube T of a length L = 15 in. is uniformly compressed by a force P acting through a rigid plate (see figure). The outside and inside diameters of the tube are 3.0 and 2.75 in., respectively. A concentric solid circular bar B of 1.5 in. diameter is mounted inside the lube. When no load is present, there is a clearance c = 0.0I0 in. between the bar B and the rigid plate. Both bar and tube are made of steel having an c[autoplastic stress-strain diagram with E = 29 X LO3 ksi and err= 36 ksi. (a) Determine the yield load Pt- and the corresponding shortening 3yof the lube. (b) Determine the plastic load Ppand the corresponding shortening Spof the tube. (c) Construct a load-displacement diagram showing the load Pas ordinate and the shortening 5 of the tube as abscissa. Hint: The load-displacement diagram is not a single straight line in the region 0 ^ P ^ Pr
Two pipe columns (AB, FC) are pin-connected to a rigid beam (BCD), as shown in the figure. Each pipe column has a modulus of E, but heights (L1or L2) and outer diameters (d1or different for each column. Assume the inner diameter of each column is 3/4 of outer diameter. Uniformly distributed downward load q = 2PIL is applied over a distance of 3L/4 along BC, and concentrated load PIA is applied downward at D. (a) Derive a formula for the displacement
A weight W = 4500 lb falls from a height h onto a vertical wood pole having length L = 15 ft, diameter d = 12 in., and modulus of elasticity E = 1.6 × 106 psi (see figure). If the allowable stress in the wood under an impact load is 2500 psi. what is the maximum permissible height h?
A steel riser pipe hangs from a drill rig. Individual segments of equal length L = 50 ft are joined to get her using bolted flange plates (see figure part b). There are six bolts at each pipe segment connection. The outer and inner pipe diameters are t2= 14 in. and d1= 13 in.; flange plate thickness tf= 1.5 in.; and boll and washer diameters are db= 1.125 in. and dn. = 1.875 in. Find the number n of permissible segments of pipe based on following allowable stresses. (a) The allowable tensile stress in the pipe is 50 ksi. (b) The allowable tensile stress in a bolt is 120 ksi. Find number of segments n for two cases: pipe hanging in air and pipe hanging in seawater.
The length of the end segments of the bar (see figure) is 20 in. and the length of the prismatic middle segment is 50 in. Also, the diameters at cross sections A. B, C, and D are 0.5, 1.0, 1.0, and 0.5 in., respectively, and the modulus of elasticity is 18 ,000 ksi. (a) Calculate the elongation of a copper bar of solid circular cross section with tapered ends when it is stretched by axial loads of magnitude 3.0 kips (see figure). (b) If the total elongation of the bar cannot exceed 0.025 in., what are the required diameters at B and C? Assume that diameters at A and D remain at 0.5 in.
A column ABC is supported at ends A and C and compressed by an axial load P (figure a). Lateral support is provided at point B but only in the plane of the figure; lateral support perpendicular to the plane of the figure is provided only at A and C. The column is constructed of two channel sections (C 6 × 8.2) back to back (see figure b). The modulus of elasticity of the column is E = 29,500 ksi and the proportional limit is 50 ksi. The height of the column is L = 15 ft. Find the allowable value of load P using a factor of safety of 2.5.
A long slender column ABC is pinned at ends A and C and compressed by an axial force F (sec figure). At the midpoint B, lateral support is provided to prevent deflection in the plane of the figure. The column is a steel wide-flange section (W 250 × 67) with E = 200 GPa. The distance between lateral supports is L = 5.5 m. Calculate the allowable load P using a factor of safety n = 2.4, taking into account the possibility of Eu 1er buckling about cither principal centroidal axis (i.e., axis 1-1 or axis 2-2).
Two steel tubes are joined at B by four pins (dp= 11 mm), as shown in the cross section a—a in the fiaure. The outer diameters of the tubes are dAB= 41 mm and dBC= 28 mm. The wall thickness are tAB= 6.5 mm and tBC= 7.5 mm. The yield stress in tension for the steel is sy = 200 MPa and the ultimate stress in tension is ??U:= 340 MPa. The corresponding yield and ultimate values in shear for the pm are 80 MPa and 140 MPa, respectively. Finally, the yield and ultimate values in bearing R between the pins and the tubes are 260 MPa, and 450 MPa, respectively. Assume that the factors safety with respect to yield stress and ultimate stress are 3.5 and 4.5. respectively. (a) Calculate the allowable tensile force P allowconsidering tension in the tube (b) Recompute P allowfor shear in the pins.(c)Finaly, recomputed Pallowfor bearing between the pm and the tubes. Which is the tubes. Which is the controlling value value of P?
The horizontal beam ABC shown in the figure is supported by columns BD and CE. The beam is prevented from moving horizontally by the pin support at end A. Each column is pinned at its upper end to the beam, but at the lower ends, support D is a sliding support and support E is pinned. Both co lu in us arc solid steel bars (E = 30 × 106 psi) of square cross section with width equal to 0.625 in. A load Q acts at distance a from column BD. If the distance a = 12 in., what is the critical value Qcr of the load? If the distance a can be varied between 0 and 40 in., what is the maximum possible value of Qcr? What is the corresponding value of the distance a?
A steel post (E=30×106) having thickness t = 1/8 in. and height L = 72 in. support a stop sign (see figure), where s = 12.5 in. The height of the post L is measured from the base to the centroid of the sign. The stop sign is subjected to wind pressure p = 20 lb/ft2 normal to its surface. Assume that the post is fixed at its base. What is the resultant load on the sign? (Sec Appendix E, Case 25, for properties of an octagon, n =8.) What is the maximum bending stress in the post? Repeat part (b) if the circular cut-outs arc eliminated over the height of the post.
A simply supported slender column is subjected to axial load P = 175 kips applied at distance e = 0,5 in. from joint s A and B (see figure). The column has a circular cross section with an outer diameter of 10 in. and wall thickness of 0.5 in. Calculate the height of the column if the maximum deflection caused by the axial loads is 0,1 in. Assume that E = 29,000 ksi.
Solve the preceding problem for a W 250 × 89 steel column having a length L = 10 m. Let E = 200 GPa.