1. A stepped cylindrical bar of cross sectional areas AAB. Agc and Ace carries five
axial forces as illustrated in Figure Q1. What is the maximum value of P for the
stresses not to exceed 100 MPa in tension and 140 MPa in compression.
c A / B +
C C T
Asc = 900.mm²
Ace = 400 mm²
2. Two plates are joined by four bolts of d = 20 mm diameter as shown in Figure
Q2. Determine the maximum load P given that the shearing, tensile and
bearing stresses are limited to 80, 100 and 140 MPa, respectively.
An aluminium alley pipe of internal diameter d' and outter diametter 0 is filled
with concrete and a compressive load P is applied to the migid cap as
illustrated in Figure Q3. What is the maximum allowable azad Par Giwem de
300 mm. o = 340 mm. E, = 70 GPa, Es = 15 GPa, (wh = so = 20
5. A steel rod of diameter 15 mm is held snugly (but without any initial stress)
between rigid walls by the arrangement shown in Figure Q5. Calculate the
temperature drop AT (degrees Celsius) at which the average shear stress in
the 12 mm diameter bolt becomes 55 MPa. (For steel use as = 12 x 10°PC and
Es = 200 GPa.)
12 mm diameter bolt
6. A 9m long steel pipe (E = 200 GPa) has an outside diameter of 220 mm and a
wall thickness of 8mm. The column is supported only at its ends and may
buckle in any direction. Calculate the critical load where the column is pinned
at both ends.
7. A solid constant-diameter shaft is subjected to the torques shown in Figure Q7.
The bearings shown allow the shaft to turn freely. If the allowable shear stress
in the shaft is 80 MPa, determine the minimum acceptable diameter for the
J= TD 37
An element in plane stress is subjected to stresses Ox = 110 MPa, a = 40 MPa and
= 30 MPa as shown in Figure Q8. Determine the stresses acting on an element
oriented at 0 = 30° from the x axis, where the angle is positive counterclockwise.
Ox1 = 118.5 MPa
Ox1 = 110.0 MPa
Oxt = 58.0 MPa
Oxt = -125.1 MPa
Okt =-22.8 MPa
Txty1" -15.3 MPa
Txty1E 30.0 MPa
Tx1y13 = -21.3 MPa
Ov1 =31,5 MPa
Oyl = 40.0 MPa
- 22.0 MPa
On = 39.1 MPa
Oy1 - 58.8 MPa
9. Determine the moment of inertia 1xx of the "Z" section about the x axis which
passes through the centroid C in Figure Q9.
1.21 X 109 mm"
124 x 106 mm
62 x 106 mm4
112 x 106 mm4
82 x 109 mm4
10. The beam-column in Figure Q10 is fixed to the floor and supports the load
shown. Determine the shear force at point B due to this loading.
11. Determine the maximum value of moment in the simple beam shown in Figure
12. Determine the distance "a" between the supports in Figure Q12 in terms of the
shafts length "L" so that the bending moment in the symmetric shaft is zero
the shaft's centre. The intensity of the distributed load at the centre of the shaft
13. Determine the shear force and bending moment at point C for the beam
illustrated in Figure Q13.
-12. 0 kNm
14. During construction of a highway bridge, the main girders are cantilevered
outwards from one pier to the next as shown in Fighure Q14. Each girder has a
cantilever length of 48m and an I-shaped cross section with dimensions as
shown in the figure. The load on each girder (during construction) is assumed
to be 9.5 kN/m, which includes the weight of the girder. Determine the
maximum bending stress in a girder due to this load.
16 A wood beam ABC with simple supports at A and B and an overhang BC is
subject to loads 3P and P acting as shown in Figure Q16. The beam has actual
dimensions 90 mm x 286 mm. Determine the maximum permissible load P
based upon an allowable shear stress in the wood of 0.7 MPa. (Disregard the
weight of the beam.)
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