Nonlinear Finite Element Analysis of Concrete Structures

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- 146 - Fig. 5.4-3: Axisymmetric finite element mesh <strong>of</strong> the Lok-Test. shown in fig. 4. The values E = 2.05*10 employed for the steel disc. MPa and v = 0.3 were -1.2 -1.0 -0.8 1-0.6 1 f/ V 1 II i i I i I ^-
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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 and 42:
- 40 - 1.0 i i 1 r 0.6 0.2 J I I L
Page 43 and 44:
Uniaxial and biaxial (
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: - 145 - Fig. 5.4-2: Punched-out pie
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 - KÎO 10 -!) cos 2 a is adde
Page 187: Sales distributors: Jul. Gjellerup,
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