# Structural Fasteners

 Question 1
A weld is used for joining an angle section ISA 100 mm x 100 mm x 10 mm to a gusset plate of thickness 15 mm to transmit a tensile load. The permissible stress in the angle is 150 MPa and the permissible shear stress on the section through the throat of the fillet weld is 108 MPa. The location of the centroid of the angle is represented by $C_{yy}$ in the figure, where $C_{yy}=28.4mm$. The area of cross-section of the angle is 1903 $mm^2$. Assuming the effective throat thickness of the weld to be 0.7 times the given weld size, the lengths $L_1$ and $L_2$ (rounded- off to the nearest integer) of the weld required to transmit a load equal to the full strength of the tension member are, respectively A 541 mm and 214 mm B 214 mm and 541 mm C 380 mm and 151 mm D 151 mm and 380 mm
GATE CE 2022 SET-1   Design of Steel Structures
Question 1 Explanation:
As per IS:800-2007 Clause no. 11.2.1
Full strength of tension member,
\begin{aligned} P&=\sigma _{at} \times A_g\\ P&=150 \times 1903\\ P&=285450N \end{aligned}
Weld strength of $L_1$,
\begin{aligned} P_1&=L_1\times (0.7 \times s) \times 108\\ P_1&=L_1\times (0.7 \times 5) \times 108\\ P_1&=378L_1 \end{aligned}
Weld strength of $L_2$,
\begin{aligned} P_2&=L_2\times (0.7 \times s) \times 108\\ P_2&=L_2\times (0.7 \times 5) \times 108\\ P_2&=378L_2 \end{aligned}
Applying moment CG equal to zero,
\begin{aligned} P_1 \times 28.4 &=P_2 \times (100-28.4)\\ \frac{P_1}{P_2}&=\frac{71.6}{28.4}\\ \frac{L_1 \times 378}{L_2 \times 378}&=\frac{71.6}{28.4}=2.521\\ L_1&=2.521L_2\\ \text{Total weld strength}&=\text{Tensile strength}\\ (L_1+L_2) \times 3.5 \times 108&=285450\\ L_1+L_2&=755.158\\ 2.521L_2+L_2&=755.152\\ L_2&=214.472mm\\ L_1&=540.685mm\\ \end{aligned}
 Question 2
A column is subjected to a total load (P) of 60 kN supported through a bracket connection, as shown in the figure (not to scale). The resultant force in bolt R (in kN,round off to one decimal place) is ________
 A 28.2 B 46.8 C 22.6 D 38.2
GATE CE 2021 SET-1   Design of Steel Structures
Question 2 Explanation:
\begin{aligned} F_{1}&=\frac{P}{n}=\frac{60}{6}=10 \mathrm{kN}\\ F_{2}&=\frac{P \cdot e}{\sum r_{i}^{2}} \times r_{R}=\frac{60 \times 100\mathrm{~mm}}{4 \times 50^{2}+2 \times 40^{2}} \times 40\\ F_{2}&=\frac{60 \times 100 \times 40}{10000+3200}=\frac{60 \times 100 \times 40}{13200}=\frac{200}{11} \mathrm{kN}\\ F_{R}&=F_{1}+F_{2}\\ &=10+\frac{200}{11}=\frac{310}{11}=28.2 \mathrm{kN} \end{aligned}
 Question 3
Two steel plates are lap jointed in a workshop using 6 mm thick fillet weld as shown in the figure (not drawn to the scale). The ultimate strength of the weld is 410 MPa. As per Limit State Design is IS 800 : 2007, the design capacity (in kN, round off to three decimal places) of the welded connection, is _______.
 A 125.547 B 653.247 C 413.586 D 212.478
GATE CE 2020 SET-2   Design of Steel Structures
Question 3 Explanation:
Design capacity of welded connection
$P_s=f_b \times l_{eff}\times t_t$ \begin{aligned} P&=\frac{410}{\sqrt{3} \times 1.25} \times 520 \times 0.7 \times 6 \\ &= \frac{716352}{\sqrt{3}}=413586N\\ &= 413.586kN \end{aligned}
 Question 4
For a channel section subjected to a downward vertical shear force at its centroid, which one of the following represents the correct distribution of shear stress in flange and web? A A B B C C D D
GATE CE 2019 SET-2   Design of Steel Structures
Question 4 Explanation:
Shear flow in horizontal member (flange) is linear with zero at free end and in vertical member (web) it is parabolic.
 Question 5
A 16 mm thick gusset plate is connected to the 12 mm thick flange plate of an I-section using fillet welds on both sides as shown in the figure. The gusset plate is subjected to a point load of 350 kN acting at a distance of 100 mm from the flange plate. Size of fillet weld is 10 mm. The maximum resultant stress (in MPa, round off to 1 decimalplace) on the fillet weld along the vertical plane would be ____
 A 86.2 B 105.3 C 115.8 D 128.6
GATE CE 2019 SET-1   Design of Steel Structures
Question 5 Explanation:
Direct concentrated load (P) = 350 kN
Eccentricity (e) = 100 mm
Depth of weld ($d_w$) at each face = 500 mm
Size of weld (S) = 10 mm
Throat thickness of weld ($t_t$) = 0.7S = 7 mm
It is a case of combined shear (P) and Bending moment (M = P.e)
Shear stress acting on weld due to direct shear force P,
\begin{aligned} (q)&=\frac{P}{A_w} \\ &= \frac{P}{2d_wt_t}\\ &=\frac{350 \times 10^3}{2 \times 500 \times 7}=50MPa \end{aligned}
Bending normal stress acting at $i^{th}$ point from Neutral axis $[f_i]=\frac{M}{I}y_i$
Maximum bending stress at extreme point in weld
\begin{aligned} [f]&=\frac{M}{I}y_{max} \\ &= \frac{Pe}{2t_t \frac{d_w^3}{12}} \times y_{max}\\ &= \frac{350 \times 10^3 \times 100}{2 \times 7 \times \frac{(500)^3}{12}} \times 250\\ &= 60MPa \end{aligned} As per IS800:2007. Maximum resultant stress an equivalent stress in fllet weld due to combined shear and bending stress
\begin{aligned} (f_{eq})&=\sqrt{f^2+3q^2} \\ &= \sqrt{60^2+3 \times 50^2}\\ &=105.3MPa \end{aligned}
 Question 6
Four bolts P, Q, R and S of equal diameter are used for a bracket subjected to a load of 130 kN as shown in the figure. The force in bolt P is
 A 32.50 kN B 69.33 kN C 82.50 kN D 119.32 kN
GATE CE 2018 SET-2   Design of Steel Structures
Question 6 Explanation: \begin{aligned} F_{1} &= \frac{P}{n}=\frac{130}{4}=32.5 kN \\ F_{2} &= \frac{Pe}{\sum r^{2}_{i}}\times r_{p} \\ r_{P} &= r_{Q} = r_{R} = r_{S} \\ &= \sqrt{50^{2}+120^{2}} \\&=130 mm \\ F_{2} &=\frac{\left ( 130\times 200 \right )\times 130}{4\times 130^{2}} \\ &= \frac{200}{4} =50 kN \\ \cos \theta &= \frac{50}{130} \\ \Rightarrow \; \; F_{R} &= \sqrt{\left [ \left ( 32.5^{2} \right )+\left ( 50^{2} \right )+\left ( 2\times 32.5\times 50 \right )\times \left ( \frac{50}{130} \right ) \right ]} \\ &= 69.33 kN \end{aligned}
 Question 7
A fillet weld is simultaneously subjected to factored normal and shear stresses of 120 MPa and 50 MPa, respectively. As per IS 800 : 2007, the equivalent stress (in MPa, up to two decimal places) is ______
 A 178.78 B 122.45 C 156.25 D 147.99
GATE CE 2018 SET-2   Design of Steel Structures
Question 7 Explanation:
Factrored normal stress, $f_{a}= 120 Mpa$
factrored shear stress, $q= 50 Mpa$
According to IS-800:2007, clause 10.5.10.1.1
The equivalent stress,
\begin{aligned} f_{e}&=\sqrt{f_{a}^{2}+3q^{2}}\leq \frac{F_{u}}{\sqrt{3}y_{mW}} \\ f_{e}&=\sqrt{120^{2}+3\times 50^{2}} \\ &=147.99 \\ \Rightarrow \;\; f_{e}& \leq \frac{f_{u}}{\sqrt{3}y_{mW}}=\frac{400}{\sqrt{3}\times 1.25} \\ &=\left ( 184.75 MPa \right )\end{aligned}
Note: The above check for combination of stresses need not be done for fillet welds where the sum of normal and shear stresses does not exceed $f_{wd}$ [clause 10.5.10.1.2(b)]. Hence, sum of normal and shear stresses $=120+50=170 MPa \leq f_{wd} (= 184.75 MPa)$
So, the above check need not be done.
So, weld is designed for a resultant shear stress of $\left ( f_{r} \right )$
\begin{aligned} f_{r}&=\sqrt{f_{a}^{2}+q^{2}} \\ &=\sqrt{120^{2}=50^{2}} \\ &=130 N/mm^{2} \end{aligned}
So, the design stress is $130 N/mm^{2}$; however equivalent stress 147.99 MPa.
 Question 8
In a fillet weld, the direct shear stress and bending tensile stress are 50 MPa and 150 MPa, respectively. As per IS 800: 2007, the equivalent stress (in MPa, up to two decimal places) will be ______
 A 122.23 B 145.56 C 173.3 D 189.54
GATE CE 2018 SET-1   Design of Steel Structures
Question 8 Explanation:
Direct bending tensile stress,
$f_{a}=150 Mpa$
Direct shear stress,
$q=50 Mpa$
According to IS 800:2007, clause 10.5.10.1.1
The equivalent stress,
\begin{aligned} f_{e}&=\sqrt{f^{2}_{a}+3q^{2}}\leq \frac{f_{u}}{\sqrt{3}\gamma _{mW}} \\ f_{e}&=\sqrt{150^{2}+3\times 50^{2}} \\&=173.21 MPa\\ \Rightarrow \;\; f_{e} & \leq \frac{f_{u}}{\sqrt{3}\gamma _{mW}} \\&=\frac{400}{\sqrt{3}\times 1.25} \\ &=184.75 MPa \end{aligned}
(Hence OK)
Note: The above check for combination of stressed need not be done for fillet welds where the sum of normal and shear stresses does not exceed $f_{wd}$ [Clause 10.5.10.1.2(b)].
Thus, $f_{a}+q=150+50=200$ MPa
$f_{a}+q \gt f_{wd}$ (= 184.75 MPa)
$\Rightarrow \;\;f_{e}= 173.21$ MPa
Thus, the weld is designed for an equivelent stress of 173.21 MPa
 Question 9
Two plates of 8 mm thickness each are connected by a fillet weld of 6 mm thickness as shown in the figure. The permissible stresses in the plate and the weld are 150 MPa and 110 MPa, respectively. Assuming the length of the weld shown in the figure to be the effective length, the permissible load P (in KN) is
 A 60 B 175.51 C 115.51 D 55.51
GATE CE 2017 SET-2   Design of Steel Structures
Question 9 Explanation:
\begin{aligned}P_{W}&=f_{b}\times l_{eff}\times t_{t} \\ &=110\left ( 100+100+50 \right )\times 0.7\times 6 \\ &=115.5\, kN \\ P_{plate}&=\sigma _{at}\times A_{net} \\ &=150\times \left ( 50\times 8 \right ) \\ &=60\, kN\end{aligned}
So permissible load = 60 kN
 Question 10
A column is subjected to a load through a bracket as shown in the figure. The resultant force (in kN, up to one decimal place) in the bolt 1 is_____
 A 3.5 B 6 C 2 D 4
GATE CE 2017 SET-1   Design of Steel Structures
Question 10 Explanation: \begin{aligned} F_{1}&=\frac{P}{n}=\frac{10}{4}=2.5kN \\ F_{2}&=\frac{Pe}{\sum r^{2}_{i}}\times r_{1} \\&=\frac{10\times 15}{4\times 5^{2}}\times 5=7.5 kN \\ F_{R}&=\sqrt{F^{2}_{1}+F_{2}^{2}+2F_{1}F_{2}\cos \theta } \\ &=\sqrt{2.5^{2}+7.5^{2}+2\times 2.5\times 7.5\times \cos 135^{\circ}} \\ &=6kN \end{aligned}
There are 10 questions to complete.

### 2 thoughts on “Structural Fasteners”

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