5003 Lectures - Faculty of Engineering and Applied Science

More documents

Recommendations

Info

E5003 - Ship Structures I 98 © C.G. Daley We can model the bulkhead frame as a pinned frame over 3 supports, subject to a lateral load; To solve this type of structure we need a method to solve indeterminate structures. What does indeterminate mean? Determinate structures have a simple set of supports, such that the support reactions can be found from considerations of rigid body equilibrium alone. This means that there are just enough supports for equilibrium to exist. This is normally 3 for 2D structures and normally 6 for 3D structures. The number of supports is also the number of equilibrium conditions that need to be satisfied. The sketch below illustrates the difference between determinate and indeterminate for a 2D beam. Determinate Indeterminate Find the Reactions Find the Reactions ⇓ ⇓ Then find the deflections Then find the deflections Reactions don’t depend on deflections The reactions depend on the deflections Equations for Reactions Equations for Reactions ⇓ ⇑⇓ coupled Equations for Deflections Equations for Deflections
E5003 - Ship Structures I 99 © C.G. Daley There are two approaches for solving indeterminate systems. Both approaches use the principle of superposition, by dividing the problem into two simpler problems, soling the simpler problems and adding the two solutions. The first method is called the Force Method (also called the Flexibility Method). The idea for the force method is; step release internal forces* or external reactions until we have one or more determinate systems step solve each determinate system, to find all reactions and deflections. Note all incompatible deflections step re-solve the determinate structures with only a set of self-balancing internal unit forces* (at internal releases) or unit reaction forces at removed reactions. This solves the system for the internal or external forces removed in . Observe the magnitude of incompatible deflections that occur per unit force. step a scale the unit forces to cause the opposite of the incompatible deflections noted in step Add solutions (everything: loads, reactions, deflections…) from and a. Note that this will result in no incompatible deflections. *note: forces include both forces and moments Overview of Force Method The structure: a beam over multiple supports: step cut the structure to have one or more determinate systems
Page 1 and 2:
Lecture Notes for Engineering 5003
Page 3 and 4:
E5003 - Ship Structures I iii © C.
Page 5 and 6:
E5003 - Ship Structures I 1 © C.G.
Page 7 and 8:
Page 9 and 10:
Page 11 and 12:
Page 13 and 14:
Page 15 and 16:
E5003 - Ship Structures I 11 © C.G
Page 17 and 18:
Page 19 and 20:
Page 21 and 22:
Page 23 and 24:
Page 25 and 26:
Page 27 and 28:
Page 29 and 30:
Page 31 and 32:
Page 33 and 34:
Page 35 and 36:
Page 37 and 38:
Page 39 and 40:
Page 41 and 42:
Page 43 and 44:
Page 45 and 46:
Page 47 and 48:
Page 49 and 50:
Page 51 and 52: E5003 - Ship Structures I 47 © C.G
Page 101: E5003 - Ship Structures I 97 © C.G
Page 105 and 106: E5003 - Ship Structures I 101 © C.
Page 153 and 154:
E5003 - Ship Structures I 149 © C.
Page 155 and 156:
Page 157 and 158:
Page 159 and 160:
Page 161 and 162:
Page 163 and 164:
Page 165 and 166:
Page 167 and 168:
Page 169 and 170:
Page 171 and 172:
Page 173 and 174:
Page 175 and 176:
Page 177 and 178:
Page 179 and 180:
Page 181 and 182:
Page 183 and 184:
Page 185 and 186:
Page 187 and 188:
Page 189 and 190:
Page 191 and 192:
Page 193 and 194:
Page 195 and 196:
Page 197 and 198:
Page 199 and 200:
Page 201 and 202:
Page 203 and 204:
Page 205 and 206:
Page 207 and 208:
Page 209 and 210:
Page 211 and 212:
Page 213 and 214:
Page 215 and 216:
Page 217 and 218:
Page 219 and 220:
Page 221 and 222:
Page 223 and 224:
Page 225 and 226:
Page 227 and 228:
Page 229 and 230:
Page 231 and 232:
Page 233 and 234:
Page 235 and 236:
Page 237:
show all

5003 Lectures - Faculty of Engineering and Applied Science

Create successful ePaper yourself

Delete template?

Save as template?