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).