#### Installation — business terrible - 1 part

September 8th, 2015

*1.1 *In fracture mechanics manuals, it is customary to use for crjv the maximum tensile stress computed elastically for an unnotchcd specimen. Express on for a beam in terms of the maximum bending moment A/, the beam depth D, and the central moment of inertia of the cross-section [. (Answer: on — M D/2I)

*1.2 *Determine on as in the previous exercise for a hollow cylindrical bar of outer diameter U and inner diameter aD (a < 1) subjected to a torsional moment Mr. (Answer: on 16Л/т/[тгІ)‘,(1 —a4)])

*1.3 *. With the same criteria as inthe previous exercises, determine o. n for a circular bar of diameter D subjected to simultaneous tension and torsion; let F be the tensile force and Mt — PPD the torque, where p is some dimensionless constant. Give the coefficient cn corresponding to Eq. (1.4.1). Hint: use Mohr’s circle to find the maximum tensile stress.

*1.4 *Results from the literature were analyzed by the authors using a characteristic specimen dimension D and a nominal stress оn defined with c, v -= 1. The results for the best fit of Bf’t and Do were 1.15 MPa and 322 mm, respectively. To compare with other results, you want to use a nominal stress defined using the same characteristic size D, but a constant c. v = 2.5. What would the values of the best-fit constants (say В f[ and Do) in this case. (Answer: Вf’t = 2.88 MPa, Do – 322 mm.)

*1.5 *Generalize the previous exercise and prove that if, for a particular selection of c. v and D, the size effect parameters arc В ft and Do, for a different selection c. v and D (where D/D — constant), their value is Bfl •= (cN/cN)Bfi and Do = (J0/D)D0.

*1.6 *Find the relationship between hj and cj that make identical Eqs. (1.4.12) and (1.4.14).

Series |
Material |
Specimen type" |
ao/D |
S/D |
b (mm) |
CN |
Reference |

АІ-А6 |
concrete |
SEN-TPB |
1/3 |
4 |
76.2 |
6 |
Walsh 1972 |

B1 |
concrete |
SEN-TPB |
1/6 |
2.5 |
38.1 |
3.75 |
Bazant and Pfeiffer 1987 |

B2 |
concrete |
DEN-F. C |
1/6 |
— |
38.1 |
1 |
Ibid. |

B3 |
concrete |
DEN-T |
1/6 |
— |
19.1 |
1 |
Ibid. |

B4 |
concrete |
DEN-S |
1/6 |
— |
38.1 |
1 |
Bazant and Pfeiffer 1986 |

Cl |
mortar |
SEN-TPB |
1/6 |
2.5 |
38.1 |
3.75 |
Bazant and Pfeiffer 1987 |

C2 |
mortar |
DEN-F. C |
1/6 |
— |
38.1 |
1 |
Ibid. |

C3 |
mortar |
DEN-T |
1/6 |
. ——— |
19.1 |
1 |
Ibid. |

C4 |
mortar |
DEN-S |
1/6 |
— |
38.1 |
1 |
Bazant and Pfeiffer 1986 |

D1 |
HSC |
SEN-TPB |
1/3 |
2.5 |
38.1 |
3.75 |
Gettu, Bazant and Karr 1990 |

El |
marble |
SEN-TPB |
.0.5 |
4 |
30 |
6 |
Fatby 1992 |

E2 |
granite |
SEN-TPB |
0.5 |
4 |
30 |
6 |
Ibid. |

FI |
limestone |
SEN-TPB |
0.4 |
4 – |
13 |
6 |
Bazant, Gettu and Kazemi 1991 |

G1 |
Si02 – |
SEN-TPB |
0.2b |
4 |
= D |
6 |
McKinney and Rice 1981° |

G2 |
SiCCN-137 |
SEN-TPB |
0.2 |
4 |
= D |
6 |
Ibid. |

G3 |
SiC CN-163 |
SEN-TPB |
0.2 |
4 |
= D |
6 |
Ibid. |

Hl-2 |
concrete |
DP |
■— |
— |
— |
0.4 |
Marti 1989 |

11 |
microcon. |
BPO |
—– —– |
— |
— |
4/тг |
Bazant and §ener 1988 |

J1 |
mortar |
UPT |
— |
— |
— |
0.75 |
Bazant, §ener and Prat 1988 |

J2 |
R. mortar |
RPT |
—– —– |
— |
— |
0.75 |
Ibid. |

K1 |
R. mortar |
LRB-UB |
— |
— |
— |
0.5 |
Bazant and Kazemi 1991 |

K2 |
R. mortar |
LRB-AB |
— |
— |
— |
0.5 |
Ibid. |

LI |
microcon. |
PS |
— |
— |
— |
1 / 7Г |
Bazant and Cao 1987 |

“See specimen types in Fig. 1.5.1. ^Variable. Results have been reduced to a fixed ao/D — 0.2. cSee also Bazant and Kazetni 1990b. |