# Bolted, Riveted and Welded Joint

 Question 1
A bracket is attached to a vertical column by means of two identical rivets $U$ and $V$ separated by a distance of $2a = 100 mm$, as shown in the figure. The permissible shear stress of the rivet material is $50 MPa$. If a load $P = 10 kN$ is applied at an eccentricity $e=3\sqrt{7}a$, the minimum crosssectional area of each of the rivets to avoid failure is ___________ $mm^2$ .
 A $800$ B $25$ C $100 \sqrt{7}$ D $200$
GATE ME 2022 SET-1   Machine Design
Question 1 Explanation:

(ii) secondary shear due to eccentricity

(i) Primary shear:
$F_p=\frac{F}{n}=\frac{10kN}{2}=5kN$
(ii) Secondary shear:
$F_s=\frac{m}{r_1^2+r_2^2} \times r =\frac{10 \times 3\sqrt{7}a}{a^2+a^2} \times a=15\sqrt{7}kN \; \; \; \; (\because a=50mm)$
Finding resultant: $R=\sqrt{F_p^2+F_s^2+2F_pF_s \cos \theta }$
Here, $\theta \text{ is }90^{\circ}$

$\therefore \;\;R_{max}=\sqrt{F_p^2+F_s^2}=\sqrt{5^2+(15\sqrt{7})^2}=40kN$
Design of Rivet: \begin{aligned} \tau _{max} &=\frac{S_{ys}}{FOS} \\ \frac{R_{max}}{A}&= \frac{50}{1}\\ \frac{40 \times 10^3}{A} &=50 \\ A&= 800 mm^2 \end{aligned}
As FOS is considered as 1, A represents the minimum cross section area required.
 Question 2
A square threaded screw is used to lift a load W by applying a force F. Efficiency of square threaded screw is expressed as
 A The ratio of work done by W per revolution to work done by F per revolution B W/F C F/W D The ratio of work done by F per revolution to work done by W per revolution
GATE ME 2022 SET-1   Machine Design
Question 2 Explanation:
$\text{Screw efficiency}=\frac{\text{Work done by the applied force/rev}}{\text{Work done in lifting the load/rev}}$
Efficiency of screw jack $\eta =\frac{\tan \alpha }{\tan(\alpha +\phi )}$
Efficiency depends on helix angle and friction angle.

 Question 3
A cantilever beam of rectangular cross-section is welded to a support by means of two fillet welds as shown in figure. A vertical load of 2 kN acts at free end of the beam. Considering that the allowable shear stress in weld is 60 $N/mm^2$, the minimum size (leg) of the weld required is _______-mm (round off to one decimal place).
 A 6.6 B 2.8 C 4.6 D 8.2
GATE ME 2021 SET-1   Machine Design
Question 3 Explanation:
\begin{aligned} \tau_{\max }=\frac{2 \times 10^{3}}{0.707 t(40) \times 2}&=\frac{35.36}{t} \mathrm{MPa} \\ \sigma_{\max }=\frac{M_{\max }}{I_{N A}} \cdot \tau_{\max } &=\frac{2000 \times 150 \times 20}{\frac{0.707 t(40)^{3} \times 2}{12}} \\ \sigma_{\max }&=\frac{795.615}{t} \mathrm{MPa}\\ \text { MSST, } \quad \sqrt{\sigma_{\max }^{2}+4 \tau^{2}} &\leq 2\left(\frac{S_{y s}}{N}\right)\\ \sqrt{\left(\frac{795.615}{t}\right)^{2}+4\left(\frac{35.36}{t}\right)^{2}} & \leq 2 \times 60 \\ \frac{798.752}{t} & \leq 2(60) \\ t &=6.65 \mathrm{~mm} \end{aligned}
 Question 4
A bolt head has to be made at the end of a rod of diameter d = 12 mm by localized forging (upsetting) operation. The length of the unsupported portion of the rod is 40 mm. To avoid buckling of the rod, a closed forging operation has to be performed with a maximum die diameter of ________ mm.
 A 12 B 18 C 40 D 24
GATE ME 2020 SET-2   Machine Design
Question 4 Explanation:
\begin{array}{l} \text { If } l \gt 3 d \text { then } \\ \qquad \begin{aligned} \text { Die dia } &=1.5 d \\ &=1.5(12) \\ &=18 \mathrm{mm} \end{aligned} \end{array}
 Question 5
A rectangular steel bar of length 500 mm, width 100 mm, and thickness 15 mm is cantilevered to a 200 mm steel channel using 4 bolts, as shown. For an external load of 10 kN applied at the tip of the steel bar, the resultant shear load on the bolt at B, is ___________ kN (round off to one decimal place).
 A 4 B 16 C 24 D 2
GATE ME 2020 SET-1   Machine Design
Question 5 Explanation: \begin{aligned} F_{A} &=F_{B}=F_{C}=F_{D}=\frac{10 \times 400}{4 \times 50 \sqrt{2}}=14.14 \mathrm{kN} \\ \text{Res}_{\mathrm{B}} &=\sqrt{14.14^{2}+2.5^{2}+2(14.14)(2.5) \cos 45} \\ \text{Res}_{\mathrm{B}} &=16.005 \mathrm{kN} \end{aligned}

There are 5 questions to complete.

### 1 thought on “Bolted, Riveted and Welded Joint”

1. The answer in the ques 20 is wrong it should be A not D as gate does not rely upon emperical formulas!