![Mechanics of Materials, 7th Edition](https://www.bartleby.com/isbn_cover_images/9780073398235/9780073398235_largeCoverImage.gif)
Concept explainers
(a)
Find the maximum deflection at point C of the cylindrical portions.
(a)
![Check Mark](/static/check-mark.png)
Answer to Problem 107P
The maximum deflection at point C of the cylindrical portions is
Explanation of Solution
Given information:
The cross sectional area AC and BC of each portions is
The modulus of elasticity (E) for portion AC is
The yield stress
The modulus of elasticity (E) for portion CB is
The yield stress
Calculation:
Calculate the displacement at point C to cause yielding of AC using the relation:
Here,
Substitute
Find the corresponding force along AC using the relation as follows:
Substitute
Find the corresponding force along CB using the relation as follows:
Substitute
Sketch the element C as shown in Figure 1.
Refer to Figure 1.
Find the value of P using equilibrium element.
Substitute
Since the applied load,
Refer to Figure 1.
Find the force along CB as follows:
Substitute
Determine the deflection at point C using the relation:
Substitute
Thus, the maximum deflection at point C of the cylindrical portions is
(b)
Find the maximum stress for each portion of rod.
(b)
![Check Mark](/static/check-mark.png)
Answer to Problem 107P
The maximum stress of rod AC is
The maximum stress of rod BC is
Explanation of Solution
Calculation:
Refer part a.
The maximum stress of rod AC is
Therefore, the maximum stress of rod AC is
Determine the maximum stress at point BC using the relation:
Substitute
Thus, the maximum stress of rod BC is
(c)
Find the permanent deflection at point C.
(c)
![Check Mark](/static/check-mark.png)
Answer to Problem 107P
The permanent deflection at point C is
Explanation of Solution
Write the expression of deflection and force for unloading as follows:
The value of
Substitute
Determine the deflection using the relation.
Substitute
Find the permanent deflection using the relation:
Substitute
Thus, the permanent deflection at point C is
Want to see more full solutions like this?
Chapter 2 Solutions
Mechanics of Materials, 7th Edition
- A steel rod of 30 mm diameter is enclosed centrally in a hollow copper tube of external diameter 40 mm and 5 mm thick. The composite bar is then subjected to an axial pull of 45 kN. If the length of the compound rod is 150 mm , and the elasticity moduli are Est = 200 GPa and Ecu = 100 GPa , determine: 1.2.2 The load carried by the rod and that carried by the tubearrow_forwardTwo tempered-steel bars, each 316316 in. thick, are bonded to a 1212 -in. mild-steel bar. This composite bar is subjected as shown to a centric axial load of magnitude P. Both steels are elastoplastic with E = 29 × 106 psi and with yield strengths equal to 100 ksi and 50 ksi, respectively, for the tempered and mild steel. Determine the residual stresses in the tempered-steel bars if the load P is gradually increased from zero to 103 kips and then decreased back to zero. The residual stress in the tempered steel bars isarrow_forwardA steel cylinder is enclosed in a bronze sleeve; both simultaneously support a vertical compressive load of 180 kN which is applied to the assembly through a horizontal bearing plate. The length of the cylinders and sleeves are equal. For the steel cylinder, A= 8000 mm2, E= 200 GPa, and α= 11.7 μm/(m°C). For the bronze sleeve, A= 16 x 103 mm2, E= 83 GPa, and α= 19.0 μm/(m°C). Compute the temperature change that will cause a zero load in the steel.arrow_forward
- 2. The steel structure shown is subjected to the load P=1000 Ib. Assume the cross-sectional area be 0.05 in?, a=10 in, R=5 in, and E=10 ×10ʻ Psi . Determine the distance between the two ends of the structure.arrow_forward1. The compound bar ABCD has a uniform cross-sectional area of 0.25 in?. When the axial force P is applied, the length of the bar is reduced by 0.018 in. Determine the magnitude of the force P. The moduli of elasticity are 29 x 10° psi for steel and 10 x 106 psi for aluminum. If bronze is used instead of aluminum, determine the length of its reduction if the same force P is applied. The modulus elasticity of bronze is 12 x 10 psi. Indicate reduction by adding the minus (-) sign in your final answer. 18 in. 6 in. 18 in. P P А Steel B C Steel Aluminumarrow_forwardThe cylindrical bar composed of two parts (AB and BC) is fixed at ends A and C. The two parts are made of different materials with different cross-sections. An external load ? =28 kN is applied at point B. The cross-sectional area of AB and BC part is 0.9 cm2and 0.3 cm2, respectively. The modulus of elasticity of the AB and BC part is 40 GPa and 200 GPa, respectively. Determine the force reactions at ends A and C.arrow_forward
- A 13-mm-diameter steel (E = 193 GPa) rod (2) is connected to a 27-mm-wide by 10-mm-thick rectangular aluminum (E = 72 GPa) bar (1), as shown. Assume L1 = 0.74 m and L2 = 1.38 m. Determine the force P (in kN rounded to the nearest tenths) required to stretch the assembly 8.1 mm.arrow_forwardThe rigid beam BC is supported by rods (1) and (2). The cross-sectional area of rod (1) is 10 mm2. The cross-sectional area of rod (2) is 19 mm2. For a uniformly distributed load of w = 3.5 kN/m, determine the length a so that the normal stress is the same in each rod. Assume L = 4.55 m.arrow_forwardA solid plastic rod has a diameter of d = 44 mm and a length of L = 700 mm. An axial load of P = 22 kN is applied to the rod as shown. The elastic modulus is E = 2.2 GPa and Poisson's ratio for this material is v=0.36. Determine the magnitude of the change in the rod diameter Ad for the given load. Larrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY
![Text book image](https://www.bartleby.com/isbn_cover_images/9780190698614/9780190698614_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9780134319650/9780134319650_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781259822674/9781259822674_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781118170519/9781118170519_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781337093347/9781337093347_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781118807330/9781118807330_smallCoverImage.gif)