# Beams

 Question 1
The flange and web plates of the doubly symmetric built-up section are connected by continuous 10 mm thick fillet welds as shown in the figure (not drawn to the scale). The moment of inertia of the section about its principal axis X-X is $7.73 \times 10^{6} mm^4$. The permissible shear stress in the fillet welds is 100 $N/ mm^2$. The design shear strength of the section is governed by the capacity of the fillet welds.

The maximum shear force (in kN, round off to one decimal place) that can be carried by the section, is _______.
 A 393.5 B 125.4 C 256.3 D 485.2
GATE CE 2020 SET-1   Design of Steel Structures
Question 1 Explanation:

q = Shear stress at the level mn in the weld = 100 MPa $=\frac{SA\bar{y}}{Ib}$
Shear force at the given section
A = Area of the cross-section above the level $mn=100 \times 10 mm^2$
$\bar{y}=$C.G. of shaded area above the level mn = 60-5 = 55 m
$I=7.73 \times 10^6 mm^4$
b = Width of weld at mn (4 welds) = 4 x t = 4 x 7 = 28 mm
t = Throat thickness
\begin{aligned} &=0.7 \times s=0.7 \times 10 \times 4=28 mm \\ 100&= \frac{F \times (100 \times 10) \times 55}{7.73 \times 10^6 \times 28}\\ F&=\frac{100 \times 7.73 \times 10^6 \times 28}{1000\times 55} \\ &=393.527kN \end{aligned}
 Question 2
A rolled I-section beam is supported on a 75 mm wide bearing plate as shown in the figure. Thicknesses of flange and web of the I-section are 20 mm and 8 mm, respectively. Root radius of the I-section is 10 mm. Assume: material yield stress, $f_y=250 MPa$ and partial safety factor for material, $\gamma _{mo}=1.10$.

As per IS: 800-2007, the web bearing strength (in kN, round off to 2 decimal places) of the beam is ________
 A 272.73 B 185.64 C 286.92 D 312.44
GATE CE 2019 SET-2   Design of Steel Structures
Question 2 Explanation:

Web bearing strength
\begin{aligned} &=[b+2.5(t_f+R)]\times t_w \times \frac{f_y}{\gamma _{mo}} \\ &= [75+2.5(20+10)] \times 8 \times \frac{250}{1.1}\\ &= 272.73kN \end{aligned}
 Question 3
Assuming that there is no possibility of shear buckling in the web, the maximum reduction permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel section due to high shear is
 A Zero B 25% C 50% D governed by the area of the flange
GATE CE 2019 SET-1   Design of Steel Structures
Question 3 Explanation:
As per IS 800 : 2007
For semi compact section
(i) In low shear case ($V \leq 0.6 V_d$)
$M_d = Z_ef_y/\gamma _{mo}$
(ii) In high shear case ($V \gt 0.6 V_d$)
$M_d = Z_ef_y/\gamma _{mo}$
So reduction is zero.
 Question 4
A steel column of ISHB 350 @72.4 kg/m is subjected to a factored axial compressive load of 2000 kN. The load is transferred to a concrete pedestal of grade M20 through a square base plate. Consider bearing strength of concrete as 0.45$f_{ck}$, where $f_{ck}$ is the characteristic strength of concrete. Using limit state method and neglecting the self weight of base plate and steel column, the length of a side of the base plate to be provided is
 A 39 cm B 42 cm C 45 cm D 48 cm
GATE CE 2018 SET-1   Design of Steel Structures
Question 4 Explanation:
\begin{aligned} &\text{Area required for base plate}\\ &=\frac{\text{Factored load}}{\text{Bearing capacity of concrete}}\\ &=\frac{2000\times 10^{3}}{0.45\times 20}=222222.222mm^{2} \end{aligned}
So, side of base plate $=\sqrt{\text{Area}}=471.4 mm= 47.14 cm$
Since, provided area must be more than required
So, answer should be 48 cm.
 Question 5
The semi-compact section of a laterally unsupported steel beam has an elastic section modulus, plastic section modulus and design bending compressive stress of $500 \; cm^3, 650 \; cm^3$ and 200MPa, respectively. The design flexural capacity (expressed in kNm) of the section is ____.
 A 1000 B 100 C 120 D 1200
GATE CE 2016 SET-1   Design of Steel Structures
Question 5 Explanation:
Design flexural capacity,
$M_{d}= \beta _{b}Z_{p}\frac{f_{y}}{\gamma _{m0}}$
$\beta _{b}= 1.0$ (for plastic and compact sections)
$\; \; \; \; = \frac{Z_{e}}{Z_{p}}$ (for semi-compact sections)
$Z_{p}=\,$ Plastic section modulus
$Z_{e}=\,$ elastic section modulus
$f_{y}=\,$ yeild stress of steel provided
$\gamma_{m0}=\,$ material factor of safety of steel against yeilding
As, design bending stress is directly given,
\begin{aligned} M_{d}&= \beta _{b}Z_{p}f_{d} \\ &= \frac{Z_{e}}{Z_{p}}\times Z_{p}\times f_{d} \\ &= Z_{e}\times f_{d} \\ &= 500\times 10^{3}\times 200\times 10^{-6} \\ &= 100 kN-m \end{aligned}
 Question 6
The figure shows a schematic representation of a steel plate girder to be used as a simply supported beam with a concentrated load. For stiffeners, PQ (running along the beam axis) and RS (running between the top and bottom flanges), which of the following pairs of statements will be TRUE?
 A (i) RS should be provided under the concentrated load only. (ii) PQ should be placed in the tension side of the flange. B (i) RS helps to prevent local buckling of the web. (ii) PQ should be placed in the compression side of the flange. C (i) RS should be provided at supports. (ii) PQ should be placed along the neutral axis. D (i) RS should be provided away from points of action of concentrated loads. (ii) PQ should be provided on the compression side of the flange.
GATE CE 2011   Design of Steel Structures
Question 6 Explanation:
PQ is a horizontal stiffener in the given plate girder. Horizontal stiffeners are also called longitudinal stiffeners. The horizontal stiffener are provided in the compression zone of the web. The first horizontal stiffener is provided at one-fifth of the distance from the compression flange to the tension flange. If required another stiffener is provided at the neutral axis. Horizontal stiffeners are not continuous and are provided between vertical stiffeners.
RS is a vertical stiffener in the given plate girder. Vertical stiffeners are also called transverse stiffeners. It is assumed that the vertical stiffener is not subjected to any load and is selected to provide necessary lateral stiffness only and can therefore, br crimped or joggled for tight fittings. Such stiffeners increase the buckling resistance of the web caused by shear.
 Question 7
An unstiffened web I-section is fabricated from a 10 mm thick plate by fillet welding as shown in the figure. If yield stress of steel is 250 MPa, the maximum shear load that section can take is
 A 750kN B 350kN C 337.5kN D 300kN
GATE CE 2005   Design of Steel Structures
Question 7 Explanation:
The web depth to thickness ratio
\begin{aligned} &=\frac{300-20}{10}=28 \lt 85 \\ \therefore \;\; V&=f_{s}t_{w}d \\ d&=300 mm, \;f_{s}=0.4f_{y} \\ f_{y}&=0.4 \times 250=100 N/mm^{2} \\ t_{W}&=10mm\\ \Rightarrow \;\; V&=100\times 10\times 300=300 kN \end{aligned}
 Question 8
A square steel slab base of area 1 $m^{2}$ is provided for a column made of two rolled channel sections. The $300mm\times 300mm$ column carries an axial compressive load of 2000 kN. The line of action of the load passes through the centroid of the column section as well as of the slab base. The permissible bending stress in slab base is 185 MPa. The required minimum thickness of the slab base is
 A 110mm B 89mm C 63mm D 55mm
GATE CE 2004   Design of Steel Structures
Question 8 Explanation:

$300mm\times 300mm$ column leaves projections as,
$\; a\, =\, b\, =\frac{1000-300}{2}\, =350mm$
Pressure on the underside of base slab
$\; W=\frac{2000}{1}=2000\, kN/m^{2}=2\, N/mm^{2}$
Thickness of slab base,
$\; t=\sqrt{\frac{3W}{F_{b}}\left ( a^{2}-\frac{b^{2}}{4} \right )}=\sqrt{\frac{3\times 2}{185}\left ( 350^{2}-\frac{350^{2}}{4} \right )}$
$\; t\simeq 55$mm
 Question 9
Group-I contains some elements in design of a simply supported plate girder and Group-II give some qualitative locations on the girder. Match the items of two lists as per good design practice and relevant codal provisions
 A P-2 Q-3 R-1 S-5 B P-4 Q-2 R-1 S-3 C P-3 Q-4 R-2 S-1 D P-1 Q-5 R-2 S-3
GATE CE 2003   Design of Steel Structures
 Question 10
An ISMB 500 is used as a beam in a multi-storey construction. From the viewpoint of structural design, it can be considered to be 'laterally restrained' when,
 A The tension flange is 'laterally restrained' B the compression flange is 'laterally restrained' C the web is adequately stiffened D the conditions in (A) and (C) are met
GATE CE 2002   Design of Steel Structures
There are 10 questions to complete.