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# UNIT-1

1. A thin rectangular plate ab is simply supported along its edges and carries a uniformly
distributed load of intensity q0. Determine the deflected form of the plate and the
distribution of bending moment.
2. Show that the deflection function
w = A (x2y2 bx2y axy2 + abxy)
is valid for a rectangular plate of sides a and b, built in on all four edges and subjected
to a uniformly distributed load of intensity q. If the material of the plate has a Youngs
modulus E and is of thickness t determine the distributions of bending moment along
the edges of the plate.
3. A rectangular plate a X b, is simply supported along each edge and carries a uniformly
distributed load of intensity q0. Assuming a deflected shape given by
w = A11 sinx a siny b
determine the value of the coefficient A11 and hence find the maximum value of
deflection.
4. A plate 10mm thick is subjected to bending moments Mx equal to 10 Nm/mm and My
equal to 5 Nm/mm. Calculate the maximum direct stresses in the plate.
5. A plate 10mm thick is subjected to bending moments Mx equal to 10 Nm/mm and My
equal to 5 Nm/mm. find the maximum twisting moment per unit length in the plate and
the direction of the planes on which this occurs.
6. A thin rectangular plate of length a and width 2a is simply supported along the edges x
=0, x =a, y=a and y=+a. The plate has a flexural rigidity D, a Poissons ratio of 0.3 and
carries a load distribution given by q(x, y)=q0 sin(x/a). If the deflection of the plate may
be represented by the expression

## w = qa4D4_1 + A coshya+ Byasinhya sinxa

Determine the values of the constants A and B.
7. A thin, elastic square plate of side a is simply supported on all four sides and supports a
uniformly distributed load q. If the origin of axes coincides with the centre of the plate
show that the deflection of the plate can be represented by the expression

where D is the flexural rigidity, is Poissons ratio and A is a constant. Calculate the
value of A and hence the central deflection of the plate.

8. Use the energy method to determine the deflected shape of a rectangular plate ab,
simply supported along each edge and carrying a concentrated load W at a position (, )
referred to axes through a corner of the plate. The deflected shape of the plate can be
represented by the series
9. A rectangular plate ab, simply supported along each edge, possesses a small initial
curvature in its unloaded state given by

Determine, using the energy method, its final deflected shape when it is subjected to a
compressive load Nx per unit length along the edges x =0, x =a.

## 10. Primary and secondary structural instability.

11. Definition of buckling load for a perfect column sketch
12. Buckling loads for different buckling modes of a pin-ended column
13. reduced modulus theory
14. tangent modulus theory
15. The pin-jointed column shown in Figure carries a compressive load P applied
eccentrically at a distance e from the axis of the column. Determine the maximum
bending moment in the column.

## 16. Shortening of a column due to buckling.

17. The total potential energy of the column in the neutral equilibrium of its buckled state
18. the general equation for the torsion of a thin-walled beam
19. A thin-walled pin-ended column is 2m long and has the cross-section shown in Figure, if
the ends of the column are free to warp determine the lowest value of axial load which
will cause buckling and specify the buckling mode. Take E =75000 N/mm2 and G=21000
N/mm2.
20. The beam shown in Fig. 9.12 is assumed to have a complete tension field web. If the
cross-sectional areas of the flanges and stiffeners are, respectively, 350mm2 and 300mm2
and the elastic section modulus of each flange is 750mm3, determine the maximum stress
in a flange and also whether or not the stiffeners will buckle. The thickness of the web is
2mm and the second moment of area of a stiffener about an axis in the plane of the web is
2000mm4; E =70 000 N/mm2.

21.

Unit-2
1. Symmetrical section beams
2. primary assumption made in determining the direct stress distribution produced by
pure bending
3. The cross-section of a beam has the dimensions shown in Figure. If the beam is subjected
to a negative bending moment of 100 kNm applied in a vertical plane, determine the
distribution of direct stress through the depth of the section.
4. A beam having the cross-section shown in Fig. 16.13 is subjected to a bending moment
of 1500Nm in a vertical plane. Calculate the maximum direct stress due to bending
stating the point at which it acts

## 5. Deflection of a cantilever beam carrying a concentrated load at its free end

6. Determine the position and magnitude of the maximum deflection in the beam of below
figure
7. Determine the horizontal and vertical components of the tip deflection of the cantilever
shown in Figure. The second moments of area of its unsymmetrical section are Ixx, Iyy
and Ixy.

8. Determine the direct stress distribution in the thin-walled Z-section shown in Figure,
produced by a positive bending moment Mx.

9. The beam section shown in Fig. 16.37 is subjected to a temperature rise of 2T0 in its
upper flange, a temperature rise of T0 in its web and zero temperature change in its lower
flange. Determine the normal force on the beam section and the moments about the
centroidal x and y axes. The beam section has aYoungs modulus E and the coefficient of
linear expansion of the material of the beam is .
10. A thin-walled, cantilever beam of unsymmetrical cross-section supports shear loads at its
free end as shown in Figure. Calculate the value of direct stress at the extremity of the
lower flange (point A) at a section half-way along the beam if the position of the shear
loads is such that no twisting of the beam occurs.

11. General stress system on element of a closed or open section beam; (b) direct stress and
shear flow system on the element.
12. Determine the shear flow distribution in the thin-walled Z-section shown in Figure, due
to a shear load Sy applied through the shear centre of the section.
13. Twist and warping of shear loaded closed section beams
14. Determine the position of the shear centre S for the thin-walled, open cross section shown
in Figure. The thickness t is constant.

15. Determination of the shear flow distribution in a closed section beam subjected to torsion
16. Displacements associated with the BredtBatho shear flow
17. Neuber beam.
18. Anapproximate solution for the torsion of a thin-walled open section beam
19. Determine the maximum shear stress and the warping distribution in the channel section
shown in Fig. 18.12 when it is subjected to an anticlockwise torque of 10Nm. G=25
000N/mm2.
20. Find the angle of twist per unit length in the wing whose cross-section is shown in Fig. 19.4 when it is
subjected to a torque of 10 kN m. Find also the maximum shear stress in the section. G=25 000
N/mm2.
Wall 12 (outer)=900 mm. Nose cell area=20 000mm2.
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