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: 
The given load is eccentric lateral load which results in

(i) primary shear due to direct loading
(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}
As secondary load is same on both rivets. Both are critical due to loading.

\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.

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