Structural Analysis : Classification of Structures Unit 1 Part 2

Que1.7. What do you mean by static indeterminacy? Explain  giving at least two  exemplifications with reference to trusses.  OR  What do you mean by static indeterminacy? Explain with  exemplifications.  AKTU 2012- 13, Marks 05  Answer  Static Indeterminacy For a structure, if available equilibrium  equations are  lower than the unknown forces  also structure is known as  statically indeterminate structure.  1. For a coplanar rigid frame structure if  3m =  3j – r Structure is statically determinate.  ii. 3m> 3j – r Structure is statically indeterminate.  where, m =  Number of members in a structure.  r =  Total number of forces and moment  response   factors. 

2. stationary indeterminacy =  3m –( 3j – r)  3. Degree of static indeterminacy for stilt =  Total number of unknowns  external and internal) forces – Number of independent equations of  equilibrium.  still, j =  Number of leg( hinge) joints connecting these If.members. 

Total number of unknown forces = ( m r)  ii. Total number of independent equilibrium equations =  2j  iii. Degree of static indeterminacy = ( m r) – 2j  exemplifications  1. For the stilt as shown inFig.1.7.1, we have  m =  18, j =  10, and r =  3. 1.7.1. Indeterminate stilt.  Degree of static indeterminacy = ( m r) – 2j  = ( 18 3) – 2 × 10  =  21 – 20 =  1  So, degree of static indeterminacy =  1.  2. For the stilt as shown in theFig.1.7.2, we have  m =  17, j =  10, and r =  4. 1.7.2.( Externally) indeterminate stilt. 

  Degree of static indeterminacy = ( m r) – 2j  = ( 17 4) – 2 × 10  =  21 – 20 =  1  So, degree of static indeterminacy =  1.  Que1.8. Explain external and internal indeterminacy of  structure.  Answer  External Indeterminacy of Structure( Ie) 

1. Let r be the total number of external  response  factors at supports  and e be the total number of equations of  stationary equilibrium available  for the given structure  also there may arise three different cases.  r =  e Structure is externally determinate. 

ii. r> e Structure is externally indeterminate. 

iii. r< e Structure is externally unstable.  therefore external indeterminacy Ie =  r –e.  Internal Indeterminacy of Structure( Ii)  It’s defined in terms of the internal member forces that can’t be  determined from simple  stationary relations if the structure is taken as  externally determinate.  ii. This type of internal indeterminacy is seen in articulated( leg joined  frames) and rigid frame structure.  iii. In case of  shafts it’s equal to zero. 

1. Articulated Structures  i. If a stilt  correspond of m number of leg connected members( it means the  stilt is having m number of unknown member forces) through ‘ j’  number of joints in the stilt where ‘ r ’ number of external support   responses are developed and ‘ e ’ number of equation of  stationary  equilibrium are available  also, 

ii. Total number of equations of equilibrium available at joints.  e =  2j( 0, V =  0) 

iii. Total number of unknown =  Internal member forces response at  supports =  m r  iv. also for determinacy of the stilt, m r =  2j or m =  2j – r  v. In case of externally determinate 2- Dimensional aeroplane

             stilt  r =  3( r =  e =  3)  hence m =  2j – 3  Total indeterminacy, It =  m –( 2j – r).( It =  Ie Ii) 

vi. For externally determinate 3 dimensional stilt  m =  3j – r( at each joint, equations available =  3j)  m =  3j – 6( r =  6)  Structural Analysis 1 – 13 C( CE- Sem- 5) 

vii. Now in case of 2- D trusses  still,  also the stilt has  fresh member and it is  If m> 2j – 3. known as  spare stilt.  m =  2j – 3, the stilt is internally determinate and is a  perfect stilt.  m< 2j – 3, the stilt is amiss stilt, it has  insufficiency of  members and its configuration is unstable  under certain  lading condition.  Degree of internal indeterminacy, Ii =  m –( 2j – 3) 

viii. In case of 3- D space trusses  still, m =  3j – 6, Internally determinate space stilt If.m> 3j – 6, Internally indeterminate space stilt  m< 3j – 6, Internally unstable stilt  Degree of internal indeterminacy, Ii =  m –( 3j – r) =  m –( 3j – 6), . Rigid Frames  i. These frames have rigid joint and may be a 2- dimensional or 3-  dimensional figure. In a member of rigid frame there  live 3 stress   effects or member forces which need to be determined.  Hence, total number of unknown = ( 3m r).  ii. Since at each joint of rigid frame three equations of equilibrium are  available  also,  Total number of equations of equilibrium =  3j  also for a frame to be internally determinate, 3j =  3m r iii.However, the frame becomes internally indeterminate, If 3m> 3j –r.  still, the frame becomes internally unstable or deficient, If 3m< 3j –r.  Ii =  3m –( 3j – r) =  3m –( 3j – 3) for 2D frame.  iv. also in case of 3 dimensional frame total number of unknown  becomes( 6m r) and a aggregate of 6j equations of equilibrium are available  for analysis.  v. also the frame will be internally determinate,  if 6j =  6m r  and if 6m> 6j – r, the frame becomes internally indeterminate  and when 6m< 6j – r, the frame becomes internally unstable.  =  6m –( 6j – r) =  6m –( 6j – 6) for 3D frame  Total Indeterminacy of Rigid Frame Structure( It)  1. A structure may be indeterminate internally or externally or both in  terms of member forces or external  responses. 

2. Hence, the total indeterminacy of a structure is the sum of internal and  external indeterminacy,  i.e., It =  le It  It = ( 3m –( 3j – r)) for 2 dimensional frame.  It = ( 6m –( 6j – r)) for 3 dimensional frame.  

Que2.1. Enumerate the different types of projected  concerted  determinate stilt with suitable  illustration and sketches.   


Explain the bracket of leg- joined determinate trusses with  the help of neat sketches.

  Answer  The following five criteria are the base for the bracket of trusses  1. According to the Shape of the Upper and Lower passions The  trusses can be classified into trusses with  resemblant  passions as shown in 2.1.1, polygonal and triangular trusses or trusses with inclined  passions  as shown inFig.2.1.2.  Upper  passion( top  passion)  Vertical  web members  slant Lower  passion  Panel 2.1.1. A stilt with  resemblant  passions.  Structural Analysis 2- 3 C( CE- Sem- 5) 2.1.2. Polygonal and triangular trusses.  2. According to the Type of the Web It permits to subdivide the trusses  into those with triangular patterns as shown inFig.2.1.3( a), those with  quadrangular patterns as shown inFig.2.1.3( b) formed by  perpendicular and   inclinations, those with the web members form a letter K as shown in Fig.2.1.3( c).  a)( b)( c) 2.1.3. Trusses according to the type of the web.  3. According to the Conditions of the Support It permits to distinguish  between the ordinary end- supported trusses as shown inFig.2.1.4( a),  the stake trusses as shown inFig.2.1.4( b), the trusses cantilevering  over one or both supports as shown inFig.2.1.4( c), and eventually crescent  or arched trusses as shown inFig.2.1.4( d) andFig.2.1.4( e).  a)( b)( c)  d)( e) 2.1.4. Trusses- depending on the type of supports.  4. According to their Purpose The trusses may be classified as roof  trusses, ground trusses, those used in crane construction.  5. According to the position of the Road  i. The trusses can be constructed so that the road is carried by the bottom   passion joints as shownFig.2.1.5( a), or the upper  passion joints as shown in Fig.2.1.5( b).  ii. occasionally the road( lane) is carried at some intermediate  position as shown  inFig.2.1.5( c).

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