Strength of Materials I - Final Exam
2007/08 Exam 1 A
CIVIL ENGINEERING 1st degree course (B. Sc.)
First Name, Surname ...............................................................
DATE ...................
Please write (draw) your solutions, only final results, in the blank space on the right side of this page.
Problem #1 (15 points)
For the bolted connection shown below calculate maximum shear and
bearing (normal) stresses in the bolts. The diameter of the bolts is
τ = ---------------------
A
700
A-A
P=20 kN
τ = .................. MPa
100
100
σ = ---------------------
500
100
100
8
20
8
σ = .................. MPa
800 [mm]
A
Problem #2 (15 points)
Draw the normal Nα, shear Tα, and
moment Mα diagrams for the given
frame.
Nα[qa]
Tα[qa]
q
a
qa
a
a
a
Mα[qa2]
Problem #3 (15 points)
Calculate maximum loading parameter P for which
normal stresses are less or equal to the given
strengths for tension RT and compression RC.
6
l
l=2m
RT = 80 MPa
RC= 130 MPa
l
1,5 Pl
20
1,5 Pl
3P
3P
2
Mα[Pl]
4,5
y
[cm]
z
11,5
2
2
Jy =
Pmax =
Problem #4 (10 points)
Calculate the shear Tα, and moment Mα at the given
cross - section α − α of the beam.
qa
qa2
qa
q
α
Tα=
α
a
a
a
a
a
a
Mα =
a
Problem #5 (20 points)
Calculate the shear force
(delamination force per unit
length) H1 and maximum
shear stress τ1 at the
segmental fillet welds for
the top flange. Assume the
weld size (thicknesses)
a1=4mm.
The moment of inertia is
[cm]
16
40kN
2
1
13.5
10kN
H1=
kN/m
τ1 =
MPa
20kN/m
A
2m
y
D
C
B
2m
2m
10.5
4
Tα[kN]
z
10
Jy=14248 cm4
8
24
Mα[kNm]
8
[mm]
Problem #6 (15 points)
Pl
Calculate the ultimate loading factor P for which the
normal stress does not exceeds the strengths:
10
tension: RT= 50 MPa
compression: RC= 150 MPa
Pl
4
P
4
y
2
l=2m
P
Pmax =
kN
Tα[P]
16
l
cm4
Jy =
z
Mα[Pl]
cm
Problem #7 (10 points)
For the unit elements (cubes) 1 and 2 located on the
surface of the shaft, show: magnitudes, directions and
signs of:
a) shear stresses,
G = 60 GPa
b) principal stresses,
l = 0.5 m
c) rotation of the right end θ.
d = 40 mm
M = 0.2 kNm
element 1 - shear stress:
element 1 - principal stress:
element 2 - shear stress:
element 2 - principal stress:
G=const
2M
2
1
2d
M
d
l
l
θ=
°
On my honor I have neither given nor received any unauthorized aid on this (exam, test, paper) - (Rice University)
Date, Signature
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