8. (a) For the sandstone of Figure 3.10, determine the value of op and Sip that best fits the peak strengths given. (The subscript p denotes "peak.")

Structural Analysis
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Chapter2: Loads On Structures
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Please answer part a
Stress- 10 psi
50
40
30
20
10
0
Stress - 10³ psi
0₁ -P
100
80
60
40
20
1000 lb/in.²
Constant ratio a,:03 15:1
Uniaxial
8
10
Axial strain-103 in./in.
(a)
Constant ratio 0₁:0₂ 8:1
-1000 psi
12
3000 psi
-2000 psi
₁. = 1 + N
qu
Uniaxial
12
16
20
Axial strain - 103 in./in.
(b)
4000 lb/in²
5000 lb/in.³
14
24
16
Lateral pressure
28
18
32
Figure 3.10 Stress difference versus axial strain curves as a function of con-
fining pressure in triaxial compression experiments on sandstone (a) and
norite (b). [From Bieniawski (1972).]
stresses are compressive. In practice, empirical curve fitting is the best proce-
dure for producing a criterion of failure tailored to any given rock type. See, for
example, Herget and Unrug (1976). A satisfactory formula for many purposes
will be afforded by the union of a tension cutoff, 3 = To, and a power law
(Bieniawski, 1974):
(3.15)
The constants N and M will be determined by fitting a curve to the family of
points
Transcribed Image Text:Stress- 10 psi 50 40 30 20 10 0 Stress - 10³ psi 0₁ -P 100 80 60 40 20 1000 lb/in.² Constant ratio a,:03 15:1 Uniaxial 8 10 Axial strain-103 in./in. (a) Constant ratio 0₁:0₂ 8:1 -1000 psi 12 3000 psi -2000 psi ₁. = 1 + N qu Uniaxial 12 16 20 Axial strain - 103 in./in. (b) 4000 lb/in² 5000 lb/in.³ 14 24 16 Lateral pressure 28 18 32 Figure 3.10 Stress difference versus axial strain curves as a function of con- fining pressure in triaxial compression experiments on sandstone (a) and norite (b). [From Bieniawski (1972).] stresses are compressive. In practice, empirical curve fitting is the best proce- dure for producing a criterion of failure tailored to any given rock type. See, for example, Herget and Unrug (1976). A satisfactory formula for many purposes will be afforded by the union of a tension cutoff, 3 = To, and a power law (Bieniawski, 1974): (3.15) The constants N and M will be determined by fitting a curve to the family of points
8. (a) For the sandstone of Figure 3.10, determine the value of op and Sip that
best fits the peak strengths given. (The subscript p denotes "peak.")
(b) Find best fit values of o, and Sir describing the residual strength of the
sandstone.
(c) Find values of M and N to express the peak strength of the sandstone in
Figure 3.10 according to Equation 3.15.
(d) Find , and Sip for the norite of Figure 3.10.
(e) Find d, and Sir for the norite.
(f) Find M and N for the norite.
Transcribed Image Text:8. (a) For the sandstone of Figure 3.10, determine the value of op and Sip that best fits the peak strengths given. (The subscript p denotes "peak.") (b) Find best fit values of o, and Sir describing the residual strength of the sandstone. (c) Find values of M and N to express the peak strength of the sandstone in Figure 3.10 according to Equation 3.15. (d) Find , and Sip for the norite of Figure 3.10. (e) Find d, and Sir for the norite. (f) Find M and N for the norite.
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