- Page 1 and 2: å Risa-R-411 Nonlinear Finite Elem
- Page 3 and 4: RISØ-R-411 NONLINEAR FINITE ELEMEN
- Page 5 and 6: CONTENTS Page PREFACE 5 1. INTRODUC
- Page 7 and 8: - 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
- Page 25 and 26: tensile and compressive meridians w
- Page 27 and 28: - 26 - ite program. A comparison wi
- Page 29 and 30: - 28 - Figure 9 contains the experi
- Page 31 and 32: - 30 - used for cyclic loading in t
- Page 33 and 34: - 32 - to that of nonlinear elastic
- Page 35 and 36: - 34 - of being proportional to the
- Page 37 and 38: - 36 - affecting the descending cur
- Page 39 and 40: - 33 - E f " I"« 4(A C -1) x {2 -
- Page 41: - 40 - 1.0 i i 1 r 0.6 0.2 J I I L
- Page 45 and 46: - 44 - -300
- Page 47 and 48: - 46 - Using Hooke's law and eq. (1
- Page 49 and 50: - 48 - stress invariant is consider
- Page 51 and 52: - 50 - as the constitutive behaviou
- Page 53 and 54: - 52 - where Hooke's law and eq. (5
- Page 55 and 56: e.. = e e . + eP (3-15) ID i] i] Fr
- Page 57 and 58: - 56 - gram is applicable for axisy
- Page 59 and 60: - p o ized in this formulation f
- Page 61 and 62: -"* — Use of Gauss's divergence t
- Page 63 and 64: - bZ - tensor c., determines the ap
- Page 65 and 66: - 64 - propriate assembly rules usi
- Page 67 and 68: - 66 - for the structure, where the
- Page 69 and 70: - 68 - where the (2 x 6) matrix w c
- Page 71 and 72: - 70 - of E and v depending on stre
- Page 73 and 74: - 72 - where the B-matrix is given
- Page 75 and 76: - 74 - Z Fig- 4.2-3: Cracking in an
- Page 77 and 78: - 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
- Page 87 and 88: - 86 - at point A, B and C are give
- Page 89 and 90: - 86 - (4.3-6) where the material
- Page 91 and 92: - 91 the reinforcement element, i.e
- Page 93 and 94:
- 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
- Page 115 and 116:
- 115 - large failure capacity when
- 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
- Page 123 and 124:
- 123 - clined cracks initiate in t
- 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
- 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 and 186:
- 155 - K^IO 10 -!) cos 2 a is adde
- Page 187:
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