Holooly Plus Logo
Holooly Plus Logo

Question 3.23:  A 3/4-in diameter steel tension rod is 5 ft long and carrie...

A  \frac{3}{4} -in-diameter steel tension rod is  5 \mathrm{ft} long and carries a load of 15 kip. Find the tensile stress, the total deformation, the unit strains, and the change in the rod diameter.

 

The Blue Check Mark means that this solution has been answered and checked by an expert. This guarantees that the final answer is accurate.
Learn more on how we answer questions.

 

\sigma=\frac{F}{A}=\frac{15000}{(\pi / 4)\left(0.75^{2}\right)}=33950 \mathrm{psi}=34.0 \mathrm{kpsi} \quad .

 

\delta=\frac{F L}{A E}=\sigma \frac{L}{E}=33950 \frac{60}{30\left(10^{6}\right)}=0.0679 in

 

\epsilon_{1}=\frac{\delta}{L}=\frac{0.0679}{60}=1130\left(10^{-6}\right)=1130 \mu \quad

 

From Table A-5,  v=0.292

 

\epsilon_{2}=-v_{\epsilon_{1}}=-0.292(1130)=-330 \mu \quad .

\Delta d=\epsilon_{2} d=-330\left(10^{-6}\right)(0.75)=-248\left(10^{-6}\right) in .

Table A-5

Material Modulus of Elasticity E Modulus of Elasticity G Poisson’s Ratio Unit Weight w
Mpsi Gpa Mpsi GPa lbf/in^{3} lbf/ft^{3} kN/m^{3}
Aluminum(all alloys) 10.4 71.7 3.9 26.9 0.333 0.098 169 26.6
Beryllium copper 18 124 7 48.3 0.285 0.297 513 80.6
Brass 15.4 106 5.82 40.1 0.324 0.309 534 83.8
Carbon steel 30 207 11.5 79.3 0.292 0.282 487 76.5
Cast iron(gray) 14.5 100 6 41.4 0.211 0.26 450 70.6
Copper 17.2 119 6.49 44.7 0.326 0.322 556 87.3
Douglas fir 1.6 11 0.6 4.1 0.33 0.016 28 4.3
Glass 6.7 46.2 2.7 18.6 0.245 0.094 162 25.4
Inconel 31 214 11 75.8 0.29 0.307 530 83.3
Lead 5.3 36.5 1.9 13.1 0.425 0.411 710 111.5
Magnesium 6.5 44.8 2.4 16.5 0.35 0.065 112 17.6
Molybdenum 48 331 17 117 0.307 0.368 636 100
Monel metal 26 179 9.5 65.5 0.32 0.319 551 86.6
Nickel silver 18.5 127 7 48.3 0.322 0.316 546 85.8
Nickel steel 30 207 11.5 79.3 0.291 0.28 484 76
Phosphor bronze 16.1 111 6 41.4 0.349 0.295 510 80.1
Stainless steel(18-8) 27.6 190 10.6 73.1 0.305 0.28 484 76
Titanium alloys 16.5 114 6.2 42.4 0.34 0.16 276 43.4

Related Answered Questions

As shown in the figure, the weight W1 strikes W2 from a height h. If W1 = 40 N, W2 = 400 N, h = 200 mm, and k = 32 kN/m, find the maximum values of the spring force and the deflection of W2 . Assume that the impact between W1 and W2 is inelastic, ignore the mass of the spring, and solve using

Verified Answer:
The drop of weight W_{1} converts p...

The table gives data concerning the shrink fit of two cylinders of differing materials and 3–119 dimensional specification in inches. Elastic constants for different materials may be found in Table A–5. Identify the radial interference δ, then find the interference pressure p, and the tangential

Verified Answer:
From Table A-5, E_{i}=30  Mpsi , E_{o}=14.5...

The table gives data concerning the shrink fit of two cylinders of differing materials and 3–119 dimensional specification in inches. Elastic constants for different materials may be found in Table A–5. Identify the radial interference δ, then find the interference pressure p, and the tangential

Verified Answer:
From Table A-5, E_{i}=10.4  Mpsi , E_{o}=30...

The table gives data concerning the shrink fit of two cylinders of differing materials and 3–119 dimensional specification in inches. Elastic constants for different materials may be found in Table A–5. Identify the radial interference δ, then find the interference pressure p, and the tangential

Verified Answer:
From Table A-5,  E_{i}=E_{o}=30  Mpsi , v_{...

The table gives data concerning the shrink fit of two cylinders of differing materials and 3–119 dimensional specification in inches. Elastic constants for different materials may be found in Table A–5. Identify the radial interference δ, then find the interference pressure p, and the tangential

Verified Answer:
From Table A-5,  E_{i}=E_{o}=30  Mpsi , v_{...

A wheel of diameter d and width w carrying a load F rolls on a flat rail. Assume that Fig. 3–39, which is based on a Poisson’s ratio of 0.3, is applicable to estimate the depth at which the maximum shear stress occurs for these materials. At this critical depth, calculate the Hertzian stresses σx ,

Verified Answer:
Note to the Instructor: The first printing incorre...

A wheel of diameter d and width w carrying a load F rolls on a flat rail. Assume that Fig. 3–39, which is based on a Poisson’s ratio of 0.3, is applicable to estimate the depth at which the maximum shear stress occurs for these materials. At this critical depth, calculate the Hertzian stresses σx ,

Verified Answer:
Use Eqs. (3-73) through (3-77). \begin{alig...

A wheel of diameter d and width w carrying a load F rolls on a flat rail. Assume that Fig. 3–39, which is based on a Poisson’s ratio of 0.3, is applicable to estimate the depth at which the maximum shear stress occurs for these materials. At this critical depth, calculate the Hertzian stresses σx ,

Verified Answer:
Use Eqs. (3-73) through (3-77). \begin{alig...

A pair of mating steel spur gears with a 0.75-in face width transmits a load of 40 lbf. For estimating the contact stresses, make the simplifying assumption that the teeth profiles can be treated as cylindrical with instantaneous radii at the contact point of interest of 0.47 in and 0.62 in,

Verified Answer:
v=0.292, E=30  Mpsi , l=0.75 \text { in, } ...

An aluminum alloy cylindrical roller with diameter 1.25 in and length 2 in rolls on the inside of a cast-iron ring having an inside radius of 6 in, which is 2 in thick. Find the maximum contact force F that can be used if the shear stress is not to exceed 4000 psi.

Verified Answer:
v_{1}=0.333, E_{1}=10.4  Mpsi , l=2 \text {...