ME 271 Strength of Materials
Midterm Exam
Question 1.
A beam consisiting of a compoiste cross section of timber and steel. Steel part is fixed to the
timber by nails. Young’s Modulus of Timber and steel are 10 GPa and 200 GPa respectively.
Assume that there is only direct shear force of 2kN acting downward as shown in the figure.
Determine the spacing between nails if allowable shear force per nail is 362 N.
V
q
VQ
shear flow
I


Q  y A  72x30000 mm3 =2160 cm3
2000 x 2160
q
 90,522( N / cm)
47723
s  Fnail / q  362 / 90,522  4cm
spacing between nails must be less than 4 cm.
Question 2.
Three forces are applied to the machine component ABD, as shown. Knowing that the cross
section containing point H is 20x40 mm rectangle, determine the principal stresses and the
maximum shearing stress at point H.
h=20 mm
H
8 mm
b=40 mm
Fx  3kN
Fy  0,5kN
Fz  2,5kN
Mx  0
M y  0.15 x 2500  375 Nm
M z  0.15x500  75Nm
A  20 x 40  800mm 2
40 x 20 3
Iz 
 26.667 x10 3 mm 4
12
x 
 xy
P My
 3000
75 x8 x10 3



 18,7 MPa
A
I
800 x10 6 26.667 x10 9
500 x(40 * 2) * 9 x10 9
2500 x(20 * 20) *10 x10 9




 5,03MPa
I zb
I yh
(40 x 20 3 / 12) x10 12 x 40 x10 3 (20 x 40 3 / 12) x10 12 x 20 x10 3
V y Qz
Vz Q y
x
18,7
 
 18,7 
2
2
 1, 2 
  x    xy 
 
  5,03
2
2
2
2


 
 1  19,97MPa
 2  1,26MPa
2
2
2
 max
 18,7 
2
 
  5,03  10,61MPa
 2 
Associate Prof. Dr Bülent EKİCİ
Head of Mechanic Deepartment
Vice Chairman in Mechnaical Engineering Dept.
Marmara Üniversity