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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
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- 8 - arbitrarily located reinforce
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- 10 - mertal data and ve will then
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- 12 - IONI = £ = OP • e = (a 1
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- 14 - 4) in accordance with 1), th
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- 16 - Fig. 2 shows the comparison
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- 18 - (1965, 1974) and of Cedolin
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- 20 - ^2 i r f~2 *! i ~" 2A " A +
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- 22 - Table 2.1-3: A.-values and t
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tensile and compressive meridians w
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- 26 - ite program. A comparison wi
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- 28 - Figure 9 contains the experi
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- 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 -
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- 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
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- 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
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- 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
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- 78 - stance one circumferential c
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- 80 - vcr v little sensitivit v to
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- 82 - ment is treated here. Howeve
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- 84 - evdn though some features of
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- 86 - at point A, B and C are give
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- 86 - (4.3-6) where the material
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- 91 the reinforcement element, i.e
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- 93 - RZ-reinforcement: =T =, f 2r
- Page 95 and 96: - 95 - identical to those for RZ-re
- Page 97 and 98: - 97 - where the same notation as i
- Page 99 and 100: - 99 - '..-here a again is given by
- Page 101 and 102: - 101 - within the element are stil
- Page 103 and 104: - 103 - now be directed towards nan
- Page 105 and 106: - 103 - total formulation as oppose
- Page 107 and 108: - 107 - question violates the failu
- Page 109 and 110: - 109 - premature failure load. How
- Page 111 and 112: - Ill - inforcement bar modelling.
- Page 113 and 114: - 113 - 600 ^ 500 t- CT uit = 518 M
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- Page 117 and 118: - 117 - that in all other structure
- Page 119 and 120: - 119 - 40 mild steel ribs with a t
- Page 121 and 122: - 121 - Fig. 5.2-4: Uppe^ surface o
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- Page 125 and 126: to no softening writer's criterion
- Page 127 and 128: - 127 - Returning *-.o the calculat
- Page 129 and 130: - 129 - the load point for both bea
- Page 131 and 132: - 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
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- Page 153 and 154: - 153 - of the resulting prediction
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- 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 and 186: - 155 - K^IO 10 -!) cos 2 a is adde
- Page 187: Sales distributors: Jul. Gjellerup,