130
CHAPTER 11. COMPOSITES
11.2. See introduction of Chapter 11.
11.4. See Section 11.1.
11.6. See Section 11.1.
11.8.
11.9.
11.10. See Section 11.2.1.
11.12. See Section 11.2.4.
11.13. Benefits of adding dispersed steel fibers to plain concrete:
xHigh energy absorption (toughness)
131
11.14. a.
Percent fibers
0
2
3
Modulus of elasticity (GPa)
30
30
30
Ultimate strength (MPa)
40
42
44
Strain at failure (m/m)
0.0021
0.0066
0.0061
Toughness (kPa)
60
165
210
Increasing the steel fibers did not change the modulus of elasticity, increased the ultimate
strength, increased the strain at failure, and increased toughness.
11.15.
% Fiber
0
2
3
Strain
Stress
(ksi)
Stress
(ksi)
Stress
(ksi)
0
0
0
0
0.001
4.5
4.5
4.5
0.002
5.7
6
6.3
0.003
5.1
6
0.004
3.5
5.5
0.005
3
5.1
0.006
2.8
4.8
132
Percent fibers
0
2
3
Modulus of elasticity (psix106)
5
5
5
Ultimate strength (ksi)
5.7
6.0
6.4
Strain at failure (in/in)
0.002
0.006
0.006
Toughness (psi)
7.2
24
30
Increasing the steel fibers did not change the modulus of elasticity, increased the ultimate
strength, increased the strain at failure, and increased toughness.
11.16. Equation 11.7, Ec= 0.65 x
0.5 x 10
6
+ 0.35 x
50 x 10
6
=17.80
x 10
6
psi
6
6
11.17. Equation 11.7, Ec= 0.55 x
0.5 x 10
6
+ 0.45 x
50 x 10
6
=22.8
x 10
6
psi
6
6
11.18. Equation 11.19,
66
66
10x 0.535.010x5065.0
10x5010x 0.5
xx
x
EE
EE
E
mffm
fm
c
QQ
=0.765
x 10
6
psi
11.20. Equation 11.7, Ec= 0.65 x 3.5 + 0.35 x 350 = 124.8 GPa
133
11.22. Eqn 11.7: Ec= vmEm+ vfEf= (1-vf) x 0.5 x 106+ 42 x 106vf
Eqn 11.8: 0.92 = 42 x 106vf/Ec
From Eqns 1 and 2, vf=0.12
11.23. Eqn 11.7: Ec= vmEm+ vfEf= (1-vf) x 2.7 + 255 vf
From Eqns 1 and 2, vf=0.34
11.24. Equation 11.21, Ec = Vm. Em+ K . Vf. Ef
The figure below shows that increasing the percent of fibers increases the modulus of
elasticity of the fiberglass.
11.25. Equation 11.21, Ec = Vm. Em+ K . Vf. Ef
6
6
)LEHUJODVV0RGXOXV
3HUFHQWRI)LEHUV