Fundamentals of Strength of Materials by Debabrata Nag, Abhijit Chanda | 9788126581276 | 8126581271 | Holooly

Mechanics of Materials

Fundamentals of Strength of Materials

235 SOLVED PROBLEMS

Question: 10.1

Calculate the strain energy of the stepped rod as shown in Figure 10.16. ...

Verified Answer:

From Eq. (10.17), we can say

U_i=\int_0^{L...

Question: 9.19

In order to measure torque applied on a shaft, we often use strain gauge to measure strain and then calculate the torque applied. Figure 9.52 shows a circular solid shaft of 96 mm diameter on which a single strain gauge is cemented at an angle of 20° with a line parallel to the axis of the shaft. ...

Verified Answer:

Let us draw the free-body diagram of the shaft as ...

Question: 9.17

The following Figure 9.45 shows the plane-stress state at a point on a certain steel structure (E = 200 GPa and G = 77 GPa). Calculate the three principal strains (a) by using stress-strain relations and (b) by using Mohr’s circle for stress to determine the principal planes and principal stresses ...

Verified Answer:

(a) We note that according to the sign convention ...

Question: 9.18

A point on a machine component has the following state of plane strain: ∈xx = -720μ, ∈yy = -400μ, γxy= +660μ If E = 700 GPa and G = 28 GPa, calculate the principal planes and the principal stresses (a) by determining the corresponding state of plane stress and then using Mohr’s circle for stress, ...

Verified Answer:

(a) We know from generalised Hooke’s law [refer to...

Question: 9.16

Using a 45° rosette shown in Figure 9.44, the strains ∈1, ∈2 and ∈3 have been determined at a point. Find out the principal strains at that point. ...

Verified Answer:

From the equation:

∈_{\theta \theta}=\bar{...

Question: 9.15

Prove that the sum of the three strain measurements made with a 60° rosette is independent of the orientation of the rosette and equal to: ∈1 + ∈2 + ∈3 = 3∈ where ∈ is the abscissa of the centre of the corresponding Mohr’s circle for strain. ...

Verified Answer:

Let the first gauge be placed at an angle q with t...

Question: 9.14

Calculate the maximum in-plane normal strain if the following strains have been obtained by the use of the rosette shown in the Figure 9.42: ∈1 = -50μ, ∈2 = +360μ, and ∈3 = +315μ ...

Verified Answer:

We know that

∈_{\theta \theta}=\bar{∈}+∈_{...

Question: 9.9

For the given state of plane strain in Figure 9.33(a), use Mohr’s circle to find (a) orientations and magnitudes of the principal strains (b) the maximum in-plane shear strain and (c) the maximum shear strain. Given that ∈xx = +60μ, ∈yy = +240 and γxy = – 50μ. ...

Verified Answer:

We again show the undeformed and deformed geometri...

Question: 9.8

The state of strain is defined as ∈xx = +5 × 10^−4, ∈yy = 3 × 10^−4 and γxy = -10.5 × 10^−4. Draw the Mohr’s circle and determine the principal strain components. ...

Verified Answer:

We first show the undeformed geometry superimposed...

Question: 9.13

Determine the strain along the x-direction if the following strains have been determined by the application of the rosette shown in Figure 9.41: ∈1 = 720μ, ∈2 = -180μ, ∈3 = 120μ ...

Verified Answer:

Using Eq. (9.109) we get strain in any direction f...

Loading...