Mechanics
Tutorial Sheet
Prob. 1: The rigid bar AB, attached to aluminum and steel rods, is
horizontal before the load P is applied. Find the vertical displacement of
point C caused by the load P = 50 kN. Neglect all weights. (Ans: 1.921mm)
Date: 17.05.2022
Prob. 2: In many situations physical constraints prevent strain from
occurring in a given direction, for example z = 0 in the case shown,
where longitudinal movement of the long prism is prevented every
point. Plane sections perpendicular to the longitudinal axis remain
plane and the same distance apart. Show that for the this situation,
which is known as plane strain, we can express  z,x and y as follows.
1
𝜎𝑧 = 𝜈(𝜎𝑥 + 𝜎𝑦 ); 𝜀𝑥 = [(1 − 𝜐2 )𝜎𝑥 − 𝜐(1 + 𝜐)𝜎𝑦 ];
𝐸
𝜀𝑦 =
Prob. 3: Links BC and DE are both made of steel (E=200 GPa) and
are 12 mm wide and 6 mm thick. Determine (a) the force in each
link when a 2.4 –kN force P is applied to the rigid member AF
shown, (b) the corresponding deflection of point A.
(Ans: FDE= - 1.6 kN, FBC= 4 kN, 𝜹𝑨 = 𝟎. 𝟎𝟓𝟔 𝒎𝒎)
1
[(1 − 𝜐2 )𝜎𝑦 − 𝜐(1 + 𝜐)𝜎𝑥 ]
𝐸
Prob. 4: A 3-mm-thick hollow polystyrene cylinder (E=3 GPa) and a rigid
circular plate (only part of which is shown) are used to support a 250mm-long steel rod AB (E=200GPa) of 6 mm diameter. If an 3.2 kN load
P is applied at B, determine (a) the elongation of rod AB, (b) the
deflection of point B, (c) the average normal stress in rod AB.
(Ans:
Prob. 5: Each of the four vertical links connecting the two
horizontal members is made of aluminum (E = 70 GPa) and has
a uniform rectangular cross-section of 10×40 𝑚𝑚. For the
loading shown, determine the deflection of (a) point E, (b) point
F and (c) point G.
,
,
)
Prob. 6: A bronze bar is fastened between a steel bar and an aluminum bar as shown in figure. Axial loads are applied at the positions
indicated. Find the largest value of P that will not exceed an overall deformation of 3.0 mm, or the following stresses: 140 MPa in the
steel, 120 MPa in the bronze, and 80 MPa in the aluminium. Assume that the assembly is suitably braced to prevent buckling. U se Est =
200 GPa, Eal = 70 GPa, and Ebr = 83 GPa.
Prob. 7: A long steel wire hanging from a balloon carries a weight W
at its lower end (see figure). The 4-mm diameter wire is 25 m long.
What is the maximum weight Wmax that can safely be carried if the
tensile yield stress for the wire is  Y = 350 MPa and a margin of safety
against yielding of 1.5 is desired? (Include the weight of the wire in
the calculations.)
Prob. 8: A steel bar of length 2.5 m with a square cross section
100 mm on each side is subjected to an axial tensile force of 1300
kN (see figure). Assume that E=200 GPa and v=0.3. Determine the
increase in volume of the bar.
Prob. 9: A plastic bar ACB having two different solid circular cross sections is held between rigid supports as shown in the figure. The
diameters in the left- and right-hand parts are 50 mm and 75 mm, respectively. The corresponding lengths are 225 mm and 300 mm.
Also, the modulus of elasticity E is 6.0 GPa, and the coefficient of thermal expansion  is 100 10-6/°C. The bar is subjected to a uniform
temperature increase of 30°C. Calculate the following quantities: (a) the compressive force P in the bar; (b) the maximum compressive
stress  c; and (c) the displacement C of point C.
Prob. 10: At room temperature (200C) a 0.5-mm gap exists between the ends of
the rods shown. At a later time the temperature has reached 140 0C , determine
(a) the normal stress in the aluminum rod
(b) the change in length of the aluminium rod.