# Tension Member

 Question 1
A steel member 'M' has reversal of stress due to live loads, whereas another member 'N' has reversal of stress due to wind load. As per IS 800:2007, the maximum slenderness ratio permitted is:
 A less for member 'M' than that of member 'N' B more for member 'M' than for member 'N' C same for both the members D not specified in the Code
GATE CE 2015 SET-2   Design of Steel Structures
Question 1 Explanation:
As per IS 800:2007 Question 2
A steel flat of rectangular section of size $70\times 6$ mm is connected to a gusset plate by three bolt each having a shear capacity of 15 kN in holes having diameter 11.5 mm. If the allowable tensile stress in the flat is 150 MPa, the maximum tension that can be applied to the flat is A 42.3kN B 52.65kN C 59.5kN D 63kN
GATE CE 2007   Design of Steel Structures
Question 2 Explanation: Along (1)-(1)
\begin{aligned} A_{net}&=\left ( 70-11.5 \right )\times 6 \\ &=351\, mm^{2} \\ P&=\left ( A_{net} \right )\times \left ( f_{y} \right ) \\ &=351\times 150 =52.65\, kN \end{aligned}
Along (2)-(2)
\begin{aligned} A_{net}&=\left ( 70-2\times 11.5 \right )\times 6 \\ &=282\, mm^{2} \\ P&=\left ( A_{net} \right )\times f_{y} \\ &=282\times 150 N=42.3 kN\end{aligned}
 Question 3
In the design of welded tension members, consider the following statements :

I. The entire cross-sectional are of the connected leg is assumed to contribute to the effective area in case of angles.
II. Two angles back-to-back and tack-welded as per the codal requirements may be assumed to behave as a tee section.
III. A check on slenderness ratio may be necessary in some cases.

The TRUE statements are
 A Only I and II B Only II and III C Only I and III D I, II and III
GATE CE 2006   Design of Steel Structures
 Question 4
The permissible stress in axial tension $\sigma _{st}$ in steel member on the net effective area of the section shall not exceed the following value ($f_{y}$ is the yield stress)
 A 0.80 $f_{y}$ B 0.75 $f_{y}$ C 0.60 $f_{y}$ D 0.50 $f_{y}$
GATE CE 2005   Design of Steel Structures
 Question 5
Two equal angles ISA $100mm\times 100mm$ of thickness 10 mm are placed back to back and connected to the either side of a gusset plate through a single row of 16 mm diameter rivets in double shear. The effective areas of the connected and unconnected legs of each of these angles are 775 m$m^{2}$ and 950 m$m^{2}$, respectively. If the angles are NOT tack riveted, the net effective area of this pair of angles is
 A 3650$mm^{2}$ B 3450$mm^{2}$ C 3076$mm^{2}$ D 2899$mm^{2}$
GATE CE 2004   Design of Steel Structures
Question 5 Explanation:
When angles are not tack riveted, they will be considered as single angles connected on one side of gusset plate,
\begin{aligned} A_{e}&=\left ( A_{1}+kA_{2} \right )\times 2 \\ k&=\frac{3A_{2}}{3A_{1}+A_{2}} \\ &=\frac{3\times 775}{3\times 775+950} \\ &=0.71 \\ A_{e}&=\left ( 775+0.71\times 950 \right )\times 2 \\ &=2899\, mm^{2}\end{aligned}
 Question 6
A truss tie consisting of 2 ISA 75x75x8 mm carries a pull of 150 kN. At ends the two angels are connected, one each on either side of a 10 mm thick gusset plate, by 18 mm diameter rivets arranged in one row. The allowable stresses in rivet are $f_s=90.0N/mm^2$ and $f_{br}=250N/mm^2$

Minimum number of rivets required at each end is
 A 2 B 3 C 4 D 5
GATE CE 2003   Design of Steel Structures
Question 6 Explanation:
Strength of rivets in shearing,
$=\frac{2\times \pi \left ( 18+1.5 \right )^{2}\times 90}{4}=53.76 kN$
Strength of rivets in bearing,
$=\left ( 18+1.5 \right )\times 10\times 250 =48.75 kN$
$\therefore$ Rivet value $=48.75 kN$
Number of rivets $=\frac{150}{48.75}=3.08 \approx 4$
 Question 7
A truss tie consisting of 2 ISA 75x75x8 mm carries a pull of 150 kN. At ends the two angels are connected, one each on either side of a 10 mm thick gusset plate, by 18 mm diameter rivets arranged in one row. The allowable stresses in rivet are $f_s=90.0N/mm^2$ and $f_{br}=250N/mm^2$

Maximum tensile stress in the tie in N/$mm^{2}$ is
 A 93.6 B 87.5 C 77.2 D 66
GATE CE 2003   Design of Steel Structures
Question 7 Explanation: (i) Assuming both thr angles as tack riveted, Gross area,
$A_{g}=\left ( 75-4 \right )\times 8\times 2=1136 mm^{2}$
For angles, connected on both sides of gussets plate, Effective area,
\begin{aligned} A_{e}&=A_{1}+kA_{2} \\ A_{1}&= \text{ Net area of connected leg} \\ &=\frac{1136}{2}-\left ( 18+1.5 \right )\times 8 \\ &=412 mm^{2} \\ A_{2}&=\text{ Area of outstanding leg} \\ &=\frac{1136}{2}=568 mm^{2} \\ k&=1.0 \\ A_{e}&=412+\left ( 1.0\times 568 \right ) \\ &=980 mm^{2} \end{aligned}
$\therefore\;\;$ Total area for both angles $=2\times 980=1960\, mm^{2}$
$\therefore$ Maximum tensile stress $=\frac{150\times 10^{2}}{1960}=76.5 N/mm^{2}$
(ii) Also assuming both the angle sections are not tack riveted,
\begin{aligned} \therefore \;\; k_{1}&=\frac{3A_{1}}{3A_{1}+A_{2}} \\ &=\frac{3\times 412}{3\times 412+568} \\ &=0.685 \\ \therefore \;\; A_{e}&=\left ( A_{1}+k_{1}A_{2} \right )\times 2 \\ &=\left ( 412+0.685\times 568 \right )\times 2 \\ &=1602.2 mm^{2} \end{aligned}
$\therefore$ Maximum tensile stress $=\frac{150\times 10^{3}}{1602.3}=93.6 N/mm^{2}$
 Question 8
ISA 100x100x10 mm (Cross sectional area = 1908 $mm^{2}$) serves as tensile member. This angle is welded to a gusset plate along A and B appropriately as shown. Assuming the yield strength of the steel to be 260 $N/mm^{2}$. The tensile strength of this member can be taken to be approximately, A 500kN B 300kN C 225kN D 375kN
GATE CE 2002   Design of Steel Structures
Question 8 Explanation: \begin{aligned} A_{1} &= 1000 \\ A_{2} &= 1000 \\ \therefore \; \; k&=\frac{3A_{1}}{3A_{1}+A_{2}}=0.75 \\ A&=A_{1}+kA_{2} \\ &=1750 mm^{2} \end{aligned}
Tensile strength of member
$=0.6\times f_{y}\times A =0.6\times 280\times 1750=273 kN$
So, tensile strength can be taken as 225 kN.
There are 8 questions to complete. 