Nonlinear Finite Element Analysis of Concrete Structures

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- lr-.G - where K 2 = K 2i-l,2i-l sin2(X - 2K 2i-l,2i sinacosa + K 2i 2± cos 2 a (B-2) Moreover - P, sina is added to element FV-i P 2 cosa is added to element F-. where P 2 ~ K 2 10 Y ~ *~ F 2i-1 sinct + F 2 COSCt ) ?>nd K 9 is given by eq. (2).
Sales distributors: Jul. Gjellerup, Sølvgade 87, DK-1307 Copenhagen K, Denmark Available on exchange from: Risø Library, Risø National Laboratory, ISBN 87-550-0649-3 P. O. Box 49, DK-4000 Roskilde, Denmark ISSN 0106-2840
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å Risa-R-411 Nonlinear Finite Elem
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RISØ-R-411 NONLINEAR FINITE ELEMEN
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CONTENTS Page PREFACE 5 1. INTRODUC
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- 5 - PREFACE This report is submit
Page 9 and 10:
- 8 - arbitrarily located reinforce
Page 11 and 12:
- 10 - mertal data and ve will then
Page 13 and 14:
- 12 - IONI = £ = OP • e = (a 1
Page 15 and 16:
- 14 - 4) in accordance with 1), th
Page 17 and 18:
- 16 - Fig. 2 shows the comparison
Page 19 and 20:
- 18 - (1965, 1974) and of Cedolin
Page 21 and 22:
- 20 - ^2 i r f~2 *! i ~" 2A " A +
Page 23 and 24:
- 22 - Table 2.1-3: A.-values and t
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tensile and compressive meridians w
Page 27 and 28:
- 26 - ite program. A comparison wi
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- 28 - Figure 9 contains the experi
Page 31 and 32:
- 30 - used for cyclic loading in t
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- 32 - to that of nonlinear elastic
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- 34 - of being proportional to the
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- 36 - affecting the descending cur
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- 33 - E f " I"« 4(A C -1) x {2 -
Page 41 and 42:
- 40 - 1.0 i i 1 r 0.6 0.2 J I I L
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Uniaxial and biaxial (
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- 44 - -300
Page 47 and 48:
- 46 - Using Hooke's law and eq. (1
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- 48 - stress invariant is consider
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- 50 - as the constitutive behaviou
Page 53 and 54:
- 52 - where Hooke's law and eq. (5
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e.. = e e . + eP (3-15) ID i] i] Fr
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- 56 - gram is applicable for axisy
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- p o ized in this formulation f
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-"* — Use of Gauss's divergence t
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- bZ - tensor c., determines the ap
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- 64 - propriate assembly rules usi
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- 66 - for the structure, where the
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- 68 - where the (2 x 6) matrix w c
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- 70 - of E and v depending on stre
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- 72 - where the B-matrix is given
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- 74 - Z Fig- 4.2-3: Cracking in an
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- 76 - retained along the crack pla
Page 79 and 80:
- 78 - stance one circumferential c
Page 81 and 82:
- 80 - vcr v little sensitivit v to
Page 83 and 84:
- 82 - ment is treated here. Howeve
Page 85 and 86:
- 84 - evdn though some features of
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- 86 - at point A, B and C are give
Page 89 and 90:
- 86 - (4.3-6) where the material
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- 91 the reinforcement element, i.e
Page 93 and 94:
- 93 - RZ-reinforcement: =T =, f 2r
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- 95 - identical to those for RZ-re
Page 97 and 98:
- 97 - where the same notation as i
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- 99 - '..-here a again is given by
Page 101 and 102:
- 101 - within the element are stil
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- 103 - now be directed towards nan
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- 103 - total formulation as oppose
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- 107 - question violates the failu
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- 109 - premature failure load. How
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- Ill - inforcement bar modelling.
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- 113 - 600 ^ 500 t- CT uit = 518 M
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- 115 - large failure capacity when
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- 117 - that in all other structure
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- 119 - 40 mild steel ribs with a t
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- 121 - Fig. 5.2-4: Uppe^ surface o
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- 123 - clined cracks initiate in t
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to no softening writer's criterion
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- 127 - Returning *-.o the calculat
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- 129 - the load point for both bea
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- 131 - max. principal ; stress loa
Page 133 and 134:
- 133 - lil loading = 21% IMM/I b)
Page 135 and 136: - 135 - loading = 26 % loading = 63
Page 137 and 138: - 137 - terized as diagonal tension
Page 139 and 140: - 139 - program utilizes the values
Page 141 and 142: - 141 - no stiffness of the concret
Page 143 and 144: - 143 - sults in a tendency to diag
Page 145 and 146: - 145 - Fig. 5.4-2: Punched-out pie
Page 147 and 148: '}sai,->(OT aqq 50 jnoxABqaq xean^o
Page 149 and 150: - 149 - tension k-0 . $&&* / t circ
Page 151 and 152: - 151 -
Page 153 and 154: - 153 - of the resulting prediction
Page 155 and 156: - i 5 T - tensile strength. As demo
Page 157 and 158: Section 2 dealt with failure and no
Page 159 and 160: - 15'J - insight into the physical
Page 161 and 162: - IS!. - obtained using the AXIPLAN
Page 163 and 164: - 163 - BAZANT, Z.P. and GAMBAROVA,
Page 165 and 166: - 1G 5 - HAND, F.R., PECKNOLD, D.A.
Page 167 and 168: - 167 - LAUNAY, P., GACHON, H. and
Page 169 and 170: - lb9 - OTTOSEN, N.S. and ANDERSEN,
Page 171 and 172: SCHIMKELPFENNIG, K. (1971). Die Fes
Page 173 and 174: - 173 - LIST OF SYMBOLS Unless othe
Page 175 and 176: - 175 - force vector due to initial
Page 177 and 178: - .17 7 - deviatoric strain tensor,
Page 179 and 180: - 179 - e* = strain in the R 1 -dir
Page 181 and 182: - 131 - ob RZ RZ = initial stress v
Page 183 and 184: — 1 f> -> _ A transformation to p
Page 185: - 155 - K^IO 10 -!) cos 2 a is adde
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Nonlinear Finite Element Analysis of Concrete Structures

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