ME1102 Mechanics of Solids - Staff.city.ac.uk

SECTION A 

Question 1 

150 

A 

2 m 

40 kN 25 kN 

B 

3 m 

C 

8 kN/m 

3m 

m 

D 

250 

All dimensions 

in mm 

15 

15 

Figure Q1(a) 

Figure Q1(b) 

The horizontal beam ABCD shown in Figure Q1(a) has a uniform cross-section as 

shown in Figure Q1(b). It is simply supported at A and D. 

(a) 

(b) 

Calculate the second moment of area, I, and the elastic section modulus, Z, for the 

beam section about its major axis. 

[3 marks] 

For the loading shown: 

(i) 

(ii) 

draw the shear force and bending moment diagrams, showing all principal 

values, 

[10 marks] 

calculate the maximum value of stress in the beam due to bending moment. 

[2 marks] 

(c) 

Sketch the distribution of shear stress in the webs of the section. 

[2 marks] 

(d) 

If the end A of the beam were fixed at the support, describe the effect this would 

have on the deflection and bending moment distribution in the beam. 

[3 marks] 

Page - 1 - of 9 

ME1102 Mechanics of Solids-May2006.doc

Question 2 

60 kN 

20 kN 

A 

B 

C 

D 

5m 

3m 

Figure Q2 

2m 

The uniform beam, ABCD, shown in Figure Q2 is simply supported at its end, A and 

propped at C. The beam carries concentrated loads of 60 kN at B and 20 kN at D. 

The modulus of elasticity of the material of the beam is 205 x 10 3 N/mm 2 and the second 

moment of area of the beam about the axis of bending is 120 x 10 6 mm 4 . 

(a) Sketch the deflected form, indicating points where the deflection, slope or 

curvature are zero. 

[2 marks] 

(b) Find the position and value of the maximum deflection of the beam. 

[18 marks] 



Question 3 

40 kN 

1.5 m 1.5 m 

40 kN 

D 

B 

A 

1.5 m 

E 

C 

Figure Q3 

The pin-jointed truss shown in Figure Q3 lies in a vertical plane and is pinned to a 

vertical, rigid support at D and E. 

(a) Find the force in each member of the truss due to the loading shown. 

[14 marks] 

(b) Find the magnitudes and directions of the reactions at D and E. 

[6 marks] 



Question 4 

(a) 

A circular, hollow shaft has a cross-section with an external diameter of 100 mm 

and wall thickness 15 mm. It has a length of 1.5 m and transmits a torque of 15 

kNm when rotating at 300 revolutions per minute. The shear modulus, G, for the 

material of the shaft is 78 x 10 3 N/mm 2 . 

Find: 

(i) the maximum shear stress in the shaft 

(ii) the angle of twist 

(iii) the power transmitted. 

[6 marks] 

[4 marks] 

[2 marks] 

(b) 

A solid circular shaft has the same length and mass. What torque would be 

transmitted if the maximum shear stress were the same as for the hollow shaft? 

[8 marks] 



SECTION B 

Question 5 

(a) Car A is travelling along a straight motorway, while car B is moving along a circular 

exit ramp of 100 m radius. The speed of A is being increased at a rate of 1.6 m/s 2 while 

car B is moving with a constant velocity of 12 m/s. For the position shown, determine: 

(i) the velocity of A relative to B and its direction (to horizontal axis) from a 

velocity vector diagram or any other method. 

[5 marks] 

(ii) the acceleration of A relative to B and its direction [7 marks] 

A 

V A = 22 m/s 

30 o 100 m 

B 

V B = 12 m/s 

Figure Q5(a) 

(b) The bar OB is supported at O and held in a vertical position by three cables AC, AD 

and BE, figure Q5(b). If the tension in the cable BE is T =453.5i -151.2j – 1209.2k, 

determine: 

(i) The magnitude of tension force. [1 marks] 

(ii) The moment of this vector T with respect to base of the pillar at O. [7 marks] 

z 

B 

A 

D 

T 

y 

C 

O 

4.5 

All dimension in m 

OB=12 m 

E 

1.5 

x 

Figure Q5 (b) 



Question 6 

The van shown in Fig. Q6 has a mass 1800 kg with mass centre at G. The coefficient of 

friction between the tyres and the road surface is 0.75. The brakes are applied when the 

van is travelling down a slop of 5 degrees and at this instant all the wheels are on the 

point of slipping. 

(a) Draw an appropriate free body diagram 

[4 marks] 

(b) Calculate: 

(i) the deceleration of the van [8 marks] 

(ii) the distance required that the van comes to rest from a speed of 100.8 km/h 

[3 marks] 

(ii) the normal forces at the front and rear wheels. [5 marks] 

100.8 km/h 

0.6 m 

G 

1.7 m 1.3 m 

θ 

= 

Figure Q6 



Question7 

The unbalanced 25 kg flywheel shown in Fig. Q7 has a radius of gyration of 0.18 m 

about an axis passing through its mass centre G. If it has a clockwise angular velocity of 

8 rad/s at the instant shown, draw the free body diagram and mass acceleration diagram. 

[5 marks] 

Also determine: 

(a) the angular acceleration of the flywheel 

[10 marks] 

(b) the horizontal and vertical reaction forces at O 

[5 marks] 

ω = 8 rad/s 

0.15 m 

120 N.m 

O 

G 

Figure Q7 



Question 8 

In the forging device shown in Fig. Q8, The 40 kg hammer is lifted to position 1 and 

released from rest. It falls and strikes a 20 kg pile embedded in the wood when it is in 

position 2. The two identical springs have a constant of k=1500 N/m, and the tension in 

each spring is 150 N when the hammer is in position 2. Neglect friction between the 

hammer and slide bars and calculate: 

(a) the unstretched length of the springs. 

[5 marks] 

(b) the velocity of the hammer just before it strikes the pile by using the conservation 

of energy . 

[10 marks] 

(c) the velocity of pile immediately after the impact if the hammer velocity is 

reduced to 1.7 m/s. 

[5 marks] 

Hammer 

1 

300 mm 

k 

k 

400 

mm 

2 

Pile 

Figure Q8 

DATA SHEET 



PART I MECHANICS OF SOLID 

One-dimensional motion 

2 

ds 

ds d s 

v = 

a = = 

2 

dt 

dt dt 

Constant velocity, a=0 s = s o +vt 

Constant Acceleration v=v o +at s=s o +v o t+ 2 

1 at 

2 

dv 

= v 

ds 

Curvilinear motion 

Cartesian (rectangular) co-ordinates 

Position vector 

r =xi+yj+zk 

Velocity vector 

v = v i+ 

x 

v y 

j+ v z 

k = x& i+ y& j+ z& k 

Acceleration 

a = a i+ 

x 

a y 

j+ a z 

k = & x& i+ & y& j+ & z& k 

Normal (n) and tangential (t) coordinates 

v 2 = v o 2 +2as 

velocity v = v e t = rω e t = rθ & e t Acceleration a = e n + v& e 

r t 

a n =v 2 2 2 

/r a t = v& =dv/dt a = a n 

+ a t 

Radial-Transverse (Polar) coordinates 

Position vector r = r e r 

Velocity vector v = r& e r + rθ & e θ 

Acceleration a = (& r& - rθ & 2 )e r + (2 r& & θ + rθ & ) e θ 

a r =( & r& - rθ & 2 ) a θ =(2 r& & θ + rθ & 2 

) a = a + 

r 

v 2 

2 

a θ 

Rigid body plane motion 

∑M G =I G α 

∑M o =I G α+ma G d 

Energy equation 

∆U= ∆KE + ∆PE+ ∆SE where ∆KE=0.5mv 2 , ∆PE =mgh and 

Strain energy SE = V e = 2 

1 k x 

2 

Kinetic energy of rigid body in plane motion KE= T = 2 

1 mvG 

2 

+ 2 

1 

ΙG ω 2 

Coefficient of Restitution 

e = 

v 

u 

B 

− 

v 

u 

A B 

= 

− 

A 

relative 

relative 

velocity 

velocity 

of 

of 

separation 

approach 

Moment of a Force 

M=r x F= (rFsinθ) 

e p

ME1102 Mechanics of Solids - Staff.city.ac.uk

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