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# structure analysis

Term | Definition |
---|---|

externally stable | It is related to support conditions.If a body is externally stable, then there will be no rigid body displacements at the supports. However, elastic displacements at supports may occur. |

minimum no. of support reactions for 2d structures and thier conditions | 3 no. of support reactions and they should be 1) non parallel 2) non concurrent 3) non trivial |

Non trivial reactions | the value of reactions should be large enough to prevent displacements. |

3 conditions of static stability/equilibrium | Sigma Fx=o Sigma Fy=o Sigma Mz= o |

1) How many for 3d stability, the reactions are required. 2) What are they. 3) They prohibit displacements in which directions. | 1) 6 reactions. 2) Sigma Fx,Fy,Fz,Mx,My,Mz=0 3) Trinagle x,y,z, Theta x,y,z. |

Other name of internal stabilty | Geometric stabilty |

What is geometric/internal stability. | According to it, no part or member of the structure should move relative to other member to preserve the geometry of the structure. But these member may have small elastic deflections. |

Conditions/requirements of geometric stability. | Minimum no. of members and their appropriate arrangement is required. |

Condition of mechanism/collapse condition | when three hinges are collinear, then this internal unstabilty occurs. |

Truss under horizontal load causes unstabilty which could be prevented by inserting which member. | one diagonal member. |

Minimum no. of members required for plane truss for internal stability. | m should be greater or equal 2J - 3. |

What is overall stable structure. | If structure is stable externally and internally. |

For overall stability which is mandatory- external or internal stabilty. | External stability. -If a structure is internally unstable but externally stable, it may or may not stable. -But if it is externally unstable but internally stable, it will definitely be unstable. |

Over stiff means. | If sufficient no.s of reactions or members are present. |

indeterminacy. | when equilibrium equations are not sufficient to find all support reactions, then structure is said to be indeterminate and the phenomenon is called indeterminacy. |

Static indeterminate/redundant/hyper static. | When the structure can be analysed using conditions of static equilibrium, the structure is said to be statically determinate structures. When all the support reactions could not be computed using equilibrium equations, the structure is called st. indet. |

Externally static indeterminacy. | It is when equilibrium equations are not able to compute all support reactions, then the structure is externally static indeterminate. |

stable and indeterminate. | when no supports displacements but supports reactions could not be computed by equilibrium equations. |

No. of support reactions- 2d 1)Fixed support 2) Hinge " 3) Roller " 4)guided roller support. | 1) 3. 2) 2. 3) 1. 4) 2. |

No. of support reactions-3d 1) 1)Fixed support 2) Hinge " 3) Roller " | 1) 6. 2) 3. 3) 1. |

1) Dse=0. 2) Dse>0. 3) Dse<0. | 1) the structure is stable and determinate. 2) the structure is stable but indeterminate. 3) the structure is not stable. |

in case of vertical loadings in beams, which reactions can be ignored. | Horizontal reactions can be ignored and ΣFx=0. |

Under inclined loadings, which reactions are ignored. | None. |

in arches, vertical loadings are ignored or not. | no. |

Internal static indeterminacy for 2d truss or plane truss (Dsi). | m-(2j-3). |

1)Dsi=0. 2) Dsi>0. 3) Dsi<0. | 1). truss is internally determinate. 2). truss is internally indeterminate. 3) truss is internally unstable. |

Internal static indeterminacy for 3d truss or space truss (Dsi). | m-(3j-6) |

1) Internal static indeterminacy for 2d rigid frame. 2) Internal static indeterminacy for 3d rigid frame. | 1) Dsi= 3C-rr. 2) Dsi= 6C-rr. |

Alternative method for total static degree of indeterminacy. 1) 2d truss. 2) 3d truss. | 1) m +re-2j. 2) m +re-3j. |

Alternative method for total static degree of indeterminacy 3) 2d rigid frame. 3) (i) when some joints are hybrid. 4) 3d rigid frame. (i) when some joints are hybrid. | 3) 3m + re - 3j (i) 3m + re - 3j - rr 4)6m + re - 6j (i) 6m + re - 6j - rr. |

kinematic degree of indeterminacy | it refers to the no.s of degree of freedom available at joints. Kinematic degree of indeterminacy is the total number of unrestrained displacement components available at all joints. |

Possible displacement components in 1) 2d rigid joint 2) 2d truss joint. 3) 3d rigid joint. 4) 3d truss joint. | 1) 3= ∆x, y, z. 2) 2= ∆x, y. 3) 6= ∆x, y, z, θx, θy, θz. |

if any of the joint is supported, what will happen | the displacement in the direction of external reaction will be prevented. |

Dk for 1) 2d truss. 2)3d truss. 3) 2d rigid frame. 4) 3d rigid frame. | 1) Dk= 2J-re 2) Dk= 3J-re. 3) Dk= 3J-re. 4) Dk= 6J-re. |

What will be Dk 1) 2d rigid frame with hybrid joints. 2) 3d rigid frame with hybrid joints. | 1) Dk= 3J-re+rr. 2) Dk= 6J-re+rr |

what will be Dk when no. of axially rigid members are also present. | 2d rigid frames Dk= 3J-re+rr-nr |