B3B072S Pages: 3

a UDL of 5 KN/m over its entire length. In addition to UDL, it carries a concentrated
load of 3 KN at its middle. Draw the shear stress distribution diagram
for the beam. (5)

PART - ^

Answer any four full questions.

. Ahorizontal girder of steel having uniform section is 14 m long and is simply supported
at its ends. It carries concentrated loads of 120 KN and 80 kN at two points 3 m and 4.5
m from the two ends respectively. I for the section of the girder is 16 x 108 mm‘ and Es
= 210 kN/mm*. Calculate the deflection of the girder at points under the two loads. Find
also the maximum deflection. (10)

10. A rectangular block of material is subjected to a tensile stress of 110 N/mm? on one
plane and a tensile stress of 47 N/mm? on a plane at right angles, together with shear
stresses of 63 N/mm’ on the same planes. Find:

(1) The direction of the principal planes. (3)
(ii) The magnitude of the principal stress (3)
(iii) The magnitude of the greatest shear stress. (4)

11. Ata point in a bracket the stresses on two mutually perpendicular planes are 120 N/mm?
and 60 N/mm? both tensile. The shear stress across these planes is 30 N/mm?.

Find using the Mohr's stress circle the

(1) Principal stresses and (5)
(11) Maximum shear stress at the point. (5)

12.A round steel rod of diameter 15 mm and length 2 m is subjected to a gradually
increasing axial compressive load. Using Euler's formula find the buckling load. Find
also the maximum lateral deflection corresponding to the buckling condition. Both ends
of the rod may be taken as hinged. Take E = 2.1 x 10° N/mm? and the yield stress

of steel = 250 N/mm”. (10)
13. a. Derive Euler's formula for a column with one end is hinged and the other end fixed.
(5)
b. Derive the differential equation for deflection curve. (5)

14. ೩. What is the change in the support condition between actual beam and conjugate

beam? (3) b. Define principal planes and principal stresses. (2)
c. Derive an expression for Rankine's crippling load for a column. (5)

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