Concept explainers
Solve the preceding problem for a steel pipe column (E = 210 GPa) with length L = 1.2 m, inner diameter d2= 36 mm, and outer diameter d2=40 mm.
i.
The critical load for the pinned-pinned end condition.
Answer to Problem 11.4.4P
The critical load for the pinned-pinned condition is 62.201 kN
Explanation of Solution
Given:
E=210 GPa
L= 1.2 m
d1= 36 mm
d2= 40 mm
Concept Used:
Calculation:
Conclusion:
The critical load for the pinned-pinned condition is 62.201 kN
ii.
The critical load for the fixed-free end condition.
Answer to Problem 11.4.4P
The critical load for the fixed-free end condition is 15.550 kN
Explanation of Solution
Given:
E=210 GPa
L= 1.2 m
d1= 36 mm
d2= 40 mm
Concept Used:
Calculation:
Conclusion:
The critical load for the fixed-free end condition is 15.550 kN
iii.
The critical load for the fixed-pinned end condition.
Answer to Problem 11.4.4P
The critical load for the fixed-pinned end condition is 127.304 kN
Explanation of Solution
Given:
E=210 GPa
L= 1.2 m
d1= 36 mm
d2= 40 mm
Concept Used:
Calculation:
Conclusion:
The critical load for the fixed-pinned end condition is 127.304 kN
iv.
The critical load for the fixed-fixed end condition.
Answer to Problem 11.4.4P
The critical load for the fixed-fixed end condition is 248.804 kN
Explanation of Solution
Given:
E=210 GPa
L= 1.2 m
d1= 36 mm
d2= 40 mm
Concept Used:
Calculation:
Conclusion:
The critical load for the fixed-fixed end condition is 248.804 kN
Want to see more full solutions like this?
Chapter 11 Solutions
Mechanics of Materials (MindTap Course List)
- A cylindrical pressure vessel having a radius r = 14 in. and wall thickness t = 0,5 in, is subjected to internal pressure p = 375 psi, In addition, a torque T = 90 kip-ft acts at each end of the cylinder (see figure), (a) Determine the maximum tensile stress ctniXand the maximum in-plane shear stress Tmjv in the wall of the cylinder. (b) If the allowable in-plane shear stress is 4.5 ksi, what is the maximum allowable torque T\ (c) If 7 = 150 kip-ft and allowable in-plane shear and allowable normal stresses are 4.5 ksi and 11.5 ksi, respectively, what is the minimum required wall thicknessarrow_forwardSolve the preceding problem for a W 250 × 89 steel column having a length L = 10 m. Let E = 200 GPa.arrow_forwardA square steel tube of a length L = 20 ft and width b2= 10.0 in. is hoisted by a crane (see figure). The lube hangs from a pin of diameter d that is held by the cables at points A and B. The cross section is a hollow square with an inner dimension b1= 8.5 in. and outer dimension b2= 10,0 in. The allowable shear stress in the pin is 8,700 psi. and the allowable bearing stress between the pin and the tube is 13,000 psi. Determine the minimum diameter of the pin in order to support the weight of the tube. Note: Disregard the rounded corners of the tube when calculating its weight.arrow_forward
- -21 Plastic bar AB of rectangular cross section (6 = 0.75 in. and h = 1.5 in.) and length L = 2 Ft is Fixed at A and has a spring support (Ar = 18 kips/in.) at C (see figure). Initially, the bar and spring have no stress. When the temperature of the bar is raised hy foot. the compressive stress on an inclined plane pq at Lq = 1.5 Ft becomes 950 psi. Assume the spring is massless and is unaffected by the temperature change. Let a = 55 × l0-6p and E = 400 ksi. (a) What is the shear stresst9 on plane pq? What is angle 07 =1 Draw a stress element oriented to plane pq, and show the stresses acting on all laces of this element. (c) If the allowable normal stress is ± 1000 psi and the allowable shear stress is ±560 psi, what is the maximum permissible value of spring constant k if the allowable stress values in the bar are not to be exceeded? (d) What is the maximum permissible length L of the bar if the allowable stress values in the bar are not be exceeded? (Assume £ = IB kips/in.) (e) What is the maximum permissible temperature increase (A7") in the bar if the allowable stress values in the bar are not to be exceeded? (Assume L = 2 ft and k = L& kips/inarrow_forwardA 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.arrow_forwardA round bar ABC of length 2L (see figure) rotates about an axis through the midpoint C with constant angular speed w (radians per second). The material of the bar has weight density y. (a) Derive a formula for the tensile stress a’ in the bar as a function of the distance x from the midpoint C. (b) What is the maximum tensile stress a max?arrow_forward
- A thin-walled circular tube and a solid circular bar of the same material (see figure) are subjected to torsion. The tube and bar have the same cross-sectional area and the same length. What is the ratio of the strain energy U1in the tube to the strain energy U2in the solid bar if the maximum shear stresses are the same in both cases? (For the tube, use the approximate theory for thin-walled bars.)arrow_forwardA semicircular bar AB lying in a horizontal plane is supported at B (sec figure part a). The bar has a centerline radius R and weight q per unit of length (total weight of the bar equals TiqR). The cross section of the bar is circular with diameter d. (a) Obtain formulas for the maximum tensile stress v maximum compressive stress c, and maximum in-plane shear stress rmdX at the top of the bar at the support due to the weight of the bar. (b) Repeat part (a) if the bar is a quarter-circular segment (see figure part b) but has the same total weight as the semicircular bar.arrow_forwardTwo 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 displacementarrow_forward
- A pressurized cylindrical tank with flat ends is loaded by torques T and tensile forces P (sec figure), The tank has a radius of r = 125 mm and wall thickness t = 6.5 mm. The internal pressure p = 7.25 MPa and the torque T = 850 N m. (a) What is the maximum permissible value of the forces P if the allowable tensile stress in the wall of the cylinder is 160 MPa? (b) If forces P = 400 kN, what is the maximum acceptable internal pressure in the tank?arrow_forward-11 A solid steel bar (G = 11.8 X 106 psi ) of diameter d = 2,0 in. is subjected to torques T = 8.0 kip-in. acting in the directions shown in the figure. Determine the maximum shear, tensile, and compressive stresses in the bar and show these stresses on sketches of properly oriented stress elements. Determine the corresponding maximum strains (shear, tensile, and compressive) in the bar and show these strains on sketches of the deformed elements.arrow_forwardAround brass bar of a diameter d1= 20mm has upset ends each with a diameter d2= 26 mm (see figure). The lengths of the segments of the bar are L1= 0.3 m and L2= 0.1 m. Quarter-circular fillets are used at the shoulders of the bar, and the modulus of elasticity of the brass is E = 100 GPa. If the bar lengthens by 0.12 mm under a tensile load P, what is the maximum stress ??maxin the bar?arrow_forward
- Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning