Products
Rewards 
from HOLOOLY

We are determined to provide the latest solutions related to all subjects FREE of charge!

Please sign up to our reward program to support us in return and take advantage of the incredible listed offers.

Enjoy Limited offers, deals & Discounts by signing up to Holooly Rewards Program

HOLOOLY 
BUSINESS MANAGER

Advertise your business, and reach millions of students around the world.

HOLOOLY 
TABLES

All the data tables that you may search for.

HOLOOLY 
ARABIA

For Arabic Users, find a teacher/tutor in your City or country in the Middle East.

HOLOOLY 
TEXTBOOKS

Find the Source, Textbook, Solution Manual that you are looking for in 1 click.

HOLOOLY 
HELP DESK

Need Help? We got you covered.

Chapter 5

Q. 5.2

A non-rotating shaft supporting a load of 2.5 kN is shown in Fig. 5.14. The shaft is made of brittle material, with an ultimate tensile strength of 300 N/mm². The factor of safety is 3. Determine the dimensions of the shaft.

Step-by-Step

Verified Solution

\text { Given } P=2.5 kN \quad S_{u t}=300 N / mm ^{2}(f s)=3 .

Step I Calculation of permissible stress

\sigma_{\max .}=\frac{S_{u t}}{(f s)}=\frac{300}{3}=100 N / mm ^{2} .

Step II Bending stress at fillet section
Due to symmetry, the reaction at each bearing is 1250 N. The stresses are critical at two sections—(i) at the centre of span, and (ii) at the fillet. At the fillet section,

\sigma_{o}=\frac{32 M_{b}}{\pi d^{3}}=\frac{32(1250 \times 350)}{\pi d^{3}} N / mm ^{2} .

\frac{D}{d}=1.1 \text { and } \frac{r}{d}=0.1 .

\text { From Fig. } 5.5, K_{t}=1.61 .

\therefore \quad \sigma_{\max .}=K_{t} \sigma_{o}=1.61\left[\frac{32(1250 \times 350)}{\pi d^{3}}\right] .

=\left(\frac{7174704.8}{d^{3}}\right) N / mm ^{2}            (i).

Step III Bending stress at centre of the span

\sigma_{o}=\frac{32 M_{b}}{\pi d^{3}}=\frac{32(1250 \times 500)}{\pi(1.1 d)^{3}} .

=\left(\frac{4783018.6}{d^{3}}\right) N / mm ^{2}           (ii).

Step IV Diameter of shaft
From (i) and (ii), it is seen that the stress is maximum at the fillet section. Equating it with permissible stress,

\left(\frac{7174704.8}{d^{3}}\right)=100 .

or            d = 41.55 mm.