Staad Stiffness and Stability Waring by Saroj Biswas

STIFNESS WARNING STAAD Pro works on the basis of Global Stiffness Matrix. For the Plane Frame Beam Shown Below, with four Degree of Freedom, allowed,a Global Stiffness Matrix will be as Below

How does a Stiffness Matrix arrived at, by allowing unit translation and Rotation along or about the axes available i.e available degree of Freedom(d.o.f). When a Joint has No Member to take rotation or Translation, it will give Zero Stiffness Warning, For Example for the Plane Frame Below , the It will Give *WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 7 EQN.NO. 12 LOADS APPLIED OR DISTRIBUTED HERE FROM ELEMENTS WILL BE IGNORED. THIS MAY BE DUE TO ALL MEMBERS AT THIS JOINT BEING RELEASED OR EFFECTIVELY RELEASED IN THIS DIRECTION.

Removal of Truss Spec from Any on of the Above Three Member will allow a Rotational Freedom, the warning will disappear. In The Figure Below, Insertion of Joint within Truss Member will cause warning as follow

*WARNING- ZERO STIFFNESS IN DIRECTION 2 AT JOINT 10 EQN.NO. 17 LOADS APPLIED OR DISTRIBUTED HERE FROM ELEMENTS WILL BE IGNORED. THIS MAY BE DUE TO ALL MEMBERS AT THIS JOINT BEING RELEASED OR EFFECTIVELY RELEASED IN THIS DIRECTION. *WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 10 EQN.NO. 18

Making Either Member 7 OR 12 as Axial- Flexural Member will make a Path for Translation along Y and Rotation about Z Axis( Since its a Plane Frame in X Y Plane, hence Translation along Z is not required and Rotation about X and Y is not required),The Warnings will Disappear. Defining the Member as Space Frame will cause Zero Stiffness in 5 Directions. Since Both Member 7 and 8 are Axial Member, Hence Cannot Translate in Z Direction, Cannot Translate in Y Direction and Cannot rotate in About X, Y, Z Direction. Since Axial Member, it can Move around X Direction. The above warning may also appear when member releases or element releases deprive the structure of stiffness at associated node along global translation or rotational direction. For the Figure 3 shown for a Plane Frame, beam 7 and 12 are released at Node 10,the Warning appears as follow

*WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 10 EQN.NO.

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LOADS APPLIED OR DISTRIBUTED HERE FROM ELEMENTS WILL BE IGNORED. THIS MAY BE DUE TO ALL MEMBERS AT THIS JOINT BEING RELEASED OR EFFECTIVELY RELEASED IN THIS DIRECTION.

STAAD treats these as warning, not Error as , if there is no force applied at or along the degree of Freeddom, the point may not be a trouble spot, as they may not necessarily be detrimental to proper transfer of load, from the Structure to Foundation, which is basic requirement for Stability of a Structure. What could be the use of Zero Stiffness warning? It could an indication of absence of Load path to foundation, causing instability in the structure. A duplicate Node Number (say node 13 and 14 have same coordinates) causes Message as Follow **WARNING- JOINT NO. 14 NOT CONNECTED. OK, IF PART OF MASTER/SLAVE. **WARNING- THIS STRUCTURE IS DISJOINTED. IGNORE IF MASTER/SLAVE OR IF UNCONNECTED JOINTS.

STABILITY ERROR Consider the Plane Frame Truss shown in the Figure 4. Although all of the Nodes creates stiffness warning, the Load 10 KN is able to find path to reach the support thru the inclined member, as the inclined members axial stiffness supports vertical load , which is transferred to this member as shear force for the Truss as a whole.

What happens if we remove the diagonal members??

*WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 1 EQN.NO. 3 LOADS APPLIED OR DISTRIBUTED HERE FROM ELEMENTS WILL BE IGNORED. THIS MAY BE DUE TO ALL MEMBERS AT THIS JOINT BEING RELEASED OR EFFECTIVELY RELEASED IN THIS DIRECTION. *WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 2 EQN.NO. 4 *WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 3 EQN.NO. 7 *WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 4 EQN.NO. 10 *WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 5 EQN.NO. 13 *WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 6 EQN.NO. 15 ***WARNING - INSTABILITY AT JOINT 4 DIRECTION = FY PROBABLE CAUSE SINGULAR-ADDING WEAK SPRING K-MATRIX DIAG= 2.6220993E+03 L-MATRIX DIAG= 0.0000000E+00 EQN NO 9 ***NOTE - VERY WEAK SPRING ADDED FOR STABILITY **NOTE** STAAD DETECTS INSTABILITIES AS EXCESSIVE LOSS OF SIGNIFICANT DIGITS DURING DECOMPOSITION. WHEN A DECOMPOSED DIAGONAL IS LESS THAN THE BUILT-IN REDUCTION FACTOR TIMES THE ORIGINAL STIFFNESS MATRIX DIAGONAL, STAAD PRINTS A SINGULARITY NOTICE. THE BUILT-IN REDUCTION FACTOR IS 1.000E-09 THE ABOVE CONDITIONS COULD ALSO BE CAUSED BY VERY STIFF OR VERY WEAK ELEMENTS AS WELL AS TRUE SINGULARITIES. ***WARNING - INSTABILITY AT JOINT 5 DIRECTION = FX PROBABLE CAUSE SINGULAR-ADDING WEAK SPRING K-MATRIX DIAG= 2.3598851E+03 L-MATRIX DIAG= 4.5474735E-13 EQN NO 11 ***NOTE - VERY WEAK SPRING ADDED FOR STABILITY

The alignment of the Members does not remain as before, the axial force from vertical member cannot find any path( Thru Force Resolution into component, thus thru diagonal members) to the Support. If the members were Axial Flexural, than Flexural Shear would have taken care of the load transfer. One way to avoid these instability, to partially release Moment of the members at ends.

All warning messages and stability error messages disappear. However we must be careful about using this method to remove error and warnings as structure may be stable in the Programme, but is not actually. We must be careful about support releases as well, a Plane Frame with pinned support analysed as space frame, we generate following error messages

***WARNING - INSTABILITY AT JOINT 6 DIRECTION = MX PROBABLE CAUSE SINGULAR-ADDING WEAK SPRING K-MATRIX DIAG= 5.2074578E+04 L-MATRIX DIAG= 4.3655746E-11 EQN NO 24 ***NOTE - VERY WEAK SPRING ADDED FOR STABILITY **NOTE** STAAD DETECTS INSTABILITIES AS EXCESSIVE LOSS OF SIGNIFICANT DIGITS DURING DECOMPOSITION. WHEN A DECOMPOSED DIAGONAL IS LESS THAN THE BUILT-IN REDUCTION FACTOR TIMES THE ORIGINAL STIFFNESS MATRIX DIAGONAL, STAAD PRINTS A SINGULARITY NOTICE. THE BUILT-IN REDUCTION FACTOR IS 1.000E-09 THE ABOVE CONDITIONS COULD ALSO BE CAUSED BY VERY STIFF OR VERY WEAK ELEMENTS AS WELL AS TRUE SINGULARITIES. ***WARNING - INSTABILITY AT JOINT 6 DIRECTION = MY PROBABLE CAUSE SINGULAR-ADDING WEAK SPRING K-MATRIX DIAG= 8.5276952E+03 L-MATRIX DIAG= -1.5825208E-10 EQN NO 25 ***NOTE - VERY WEAK SPRING ADDED FOR STABILITY

A Space frame with all support having FX, FY , FZ released will generate following Error messages ***WARNING - INSTABILITY AT JOINT 11 DIRECTION = FX PROBABLE CAUSE SINGULAR-ADDING WEAK SPRING K-MATRIX DIAG= 4.3827921E+01 L-MATRIX DIAG= 5.4001248E-13 EQN NO ***NOTE - VERY WEAK SPRING ADDED FOR STABILITY

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**NOTE** STAAD DETECTS INSTABILITIES AS EXCESSIVE LOSS OF SIGNIFICANT DIGITS DURING DECOMPOSITION. WHEN A DECOMPOSED DIAGONAL IS LESS THAN THE BUILT-IN REDUCTION FACTOR TIMES THE ORIGINAL STIFFNESS MATRIX DIAGONAL, STAAD PRINTS A SINGULARITY NOTICE. THE BUILT-IN REDUCTION FACTOR IS 1.000E-09 THE ABOVE CONDITIONS COULD ALSO BE CAUSED BY VERY STIFF OR VERY WEAK ELEMENTS AS WELL AS TRUE SINGULARITIES. ***WARNING - INSTABILITY AT JOINT 11 DIRECTION = FY PROBABLE CAUSE SINGULAR-ADDING WEAK SPRING K-MATRIX DIAG= 2.6220993E+03 L-MATRIX DIAG= 0.0000000E+00 EQN NO 47 ***NOTE - VERY WEAK SPRING ADDED FOR STABILITY ***WARNING - INSTABILITY AT JOINT 11 DIRECTION = FZ PROBABLE CAUSE SINGULAR-ADDING WEAK SPRING K-MATRIX DIAG= 4.3827921E+01 L-MATRIX DIAG= 8.5265128E-14 EQN NO 48 ***NOTE - VERY WEAK SPRING ADDED FOR STABILITY

Making any one of them as pinned or Fixed will create a load path, Error messages will disappear. Now consider the Plane Frame Portal. While increasing the Stiffness of shaded part 1 0 times , generates no warning, while increasing it by 100 times, generate warning as below ** WARNING ** A STIFF MATERIAL WITH 1.086E+01 TIMES THE STIFFNESS OF STEEL ENTERED. PLEASE CHECK.

Which is some times done to simulate rigidity of beam column junctions in RCC, which is OK

Increasing Stiffness of Shaded part by 100,000, 000 times causes Error Messages for all the 6 Degree of Freedom for the Joints under consideration. This is due to numerical instability in matrix decomposition, at joint one of the Term becomes, Term= 1/(1F), where F= EI1/(EI1+EI2), resulting F=1, Term =1/(1-1)=1/0. These Types of Error may also results from the mistakes done in unit , say same Numerical value of one beam Witten as MMS Newton as 1000, an other beam in M KN witten as 10,000( which actually 10, 000 mm). Also may arise when very stiff properties are Assigned to member connecting to a another member( Flexible Member).

**NOTE - NEAR INSTABILITY AT JOINT 7 DIRECTION = FX PROBABLE CAUSE - NEAR SINGULAR K-MATRIX K-MATRIX DIAG= 9.9134905E+11 L-MATRIX DIAG= 5.9138909E+03 EQN NO 13 **NOTE** STAAD DETECTS INSTABILITIES AS EXCESSIVE LOSS OF SIGNIFICANT DIGITS DURING DECOMPOSITION. WHEN A DECOMPOSED DIAGONAL IS LESS THAN THE BUILT-IN REDUCTION FACTOR TIMES THE ORIGINAL STIFFNESS MATRIX DIAGONAL, STAAD PRINTS A SINGULARITY NOTICE. THE BUILT-IN REDUCTION FACTOR IS 1.000E-09 THE ABOVE CONDITIONS COULD ALSO BE CAUSED BY VERY STIFF OR VERY WEAK ELEMENTS AS WELL AS TRUE SINGULARITIES. STAAD SPACE -- PAGE NO. 3 **NOTE - NEAR INSTABILITY AT JOINT 7 DIRECTION = FY PROBABLE CAUSE - NEAR SINGULAR K-MATRIX K-MATRIX DIAG= 3.7204753E+12 L-MATRIX DIAG= 8.1625132E+03 EQN NO ***WARNING - INSTABILITY AT JOINT 7 DIRECTION = FZ PROBABLE CAUSE SINGULAR-ADDING WEAK SPRING K-MATRIX DIAG= 3.7717512E+11 L-MATRIX DIAG= 6.9449280E+01 EQN NO ***NOTE - VERY WEAK SPRING ADDED FOR STABILITY **NOTE - NEAR INSTABILITY AT JOINT 7 DIRECTION = MX PROBABLE CAUSE - NEAR SINGULAR K-MATRIX K-MATRIX DIAG= 1.3679023E+14 L-MATRIX DIAG= 4.5783027E+05 EQN NO **NOTE - NEAR INSTABILITY AT JOINT 7 DIRECTION = MY PROBABLE CAUSE - NEAR SINGULAR K-MATRIX K-MATRIX DIAG= 5.6494873E+13 L-MATRIX DIAG= 3.7803318E+05 EQN NO **NOTE - NEAR INSTABILITY AT JOINT 7 DIRECTION = MZ PROBABLE CAUSE - NEAR SINGULAR K-MATRIX K-MATRIX DIAG= 5.5341489E+14 L-MATRIX DIAG= 4.8779121E+06 EQN NO ***WARNING - INSTABILITY AT JOINT 8 DIRECTION = FX PROBABLE CAUSE SINGULAR-ADDING WEAK SPRING K-MATRIX DIAG= 9.9134905E+11 L-MATRIX DIAG= 4.8857324E+02 EQN NO ***NOTE - VERY WEAK SPRING ADDED FOR STABILITY **NOTE - NEAR INSTABILITY AT JOINT 8 DIRECTION = FY PROBABLE CAUSE - NEAR SINGULAR K-MATRIX K-MATRIX DIAG= 3.7204753E+12 L-MATRIX DIAG= 8.1300679E+03 EQN NO ***WARNING - INSTABILITY AT JOINT 8 DIRECTION = FZ PROBABLE CAUSE SINGULAR-ADDING WEAK SPRING K-MATRIX DIAG= 3.7717512E+11 L-MATRIX DIAG= 6.0517456E+01 EQN NO ***NOTE - VERY WEAK SPRING ADDED FOR STABILITY **NOTE - NEAR INSTABILITY AT JOINT 8 DIRECTION = MX PROBABLE CAUSE - NEAR SINGULAR K-MATRIX K-MATRIX DIAG= 1.3679023E+14 L-MATRIX DIAG= 4.3902155E+05 EQN NO **NOTE - NEAR INSTABILITY AT JOINT 8 DIRECTION = MY PROBABLE CAUSE K-MATRIX DIAG= 5.6494873E+13 L-MATRIX DIAG= 3.3535532E+05 EQN NO **NOTE - NEAR INSTABILITY AT JOINT 8 DIRECTION = MZ PROBABLE CAUSE - NEAR SINGULAR K-MATRIX K-MATRIX DIAG= 5.5341489E+14 L-MATRIX DIAG= 4.2073266E+06 EQN NO

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Consider the Space Frame Shown in Figure 9. The Perform Analysis would results in following Error Messages

***WARNING - INSTABILITY AT JOINT 6 DIRECTION = MY PROBABLE CAUSE SINGULAR-ADDING WEAK SPRING K-MATRIX DIAG= 4.2638473E+03 L-MATRIX DIAG= 0.0000000E+00 EQN NO 20 ***NOTE - VERY WEAK SPRING ADDED FOR STABILITY **NOTE** STAAD DETECTS INSTABILITIES AS EXCESSIVE LOSS OF SIGNIFICANT DIGITS DURING DECOMPOSITION. WHEN A DECOMPOSED DIAGONAL IS LESS THAN THE BUILT-IN REDUCTION FACTOR TIMES THE ORIGINAL STIFFNESS MATRIX DIAGONAL, STAAD PRINTS A SINGULARITY NOTICE. THE BUILT-IN REDUCTION FACTOR IS 1.000E-09 THE ABOVE CONDITIONS COULD ALSO BE CAUSED BY VERY STIFF OR VERY WEAK ELEMENTS AS WELL AS TRUE SINGULARITIES. ***WARNING - INSTABILITY AT JOINT 7 DIRECTION = MY PROBABLE CAUSE SINGULAR-ADDING WEAK SPRING K-MATRIX DIAG= 4.2638473E+03 L-MATRIX DIAG= 0.0000000E+00 EQN NO 26 ***NOTE - VERY WEAK SPRING ADDED FOR STABILITY ***WARNING - INSTABILITY AT JOINT 8 DIRECTION = MX PROBABLE CAUSE SINGULAR-ADDING WEAK SPRING K-MATRIX DIAG= 2.7275058E+04 L-MATRIX DIAG= -8.5856300E-10 EQN NO 31 ***NOTE - VERY WEAK SPRING ADDED FOR STABILITY ***WARNING - INSTABILITY AT JOINT 8 DIRECTION = MY

PROBABLE CAUSE SINGULAR-ADDING WEAK SPRING K-MATRIX DIAG= 4.2638473E+03 L-MATRIX DIAG= 0.0000000E+00 EQN NO ***NOTE - VERY WEAK SPRING ADDED FOR STABILITY ***WARNING - INSTABILITY AT JOINT 8 DIRECTION = MZ PROBABLE CAUSE SINGULAR-ADDING WEAK SPRING K-MATRIX DIAG= 2.7275058E+04 L-MATRIX DIAG= -8.5856300E-10 EQN NO ***NOTE - VERY WEAK SPRING ADDED FOR STABILITY

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The Joint 5 which has fixed base at 1, is able to take both MX and MZ. In Joint 6 and 7, MX and MZ is being catered by Joint 5 (Via Fixed base at Joint 1). But joint 8 is Not able to take all three d.o.f MX, MY, MZ. Consider the Figure Below.

It will give following Errors ***WARNING - INSTABILITY AT JOINT 8 DIRECTION = MZ PROBABLE CAUSE SINGULAR-ADDING WEAK SPRING K-MATRIX DIAG= 1.9802713E+07 L-MATRIX DIAG= 0.0000000E+00 EQN NO 36 ***NOTE - VERY WEAK SPRING ADDED FOR STABILITY **NOTE** STAAD DETECTS INSTABILITIES AS EXCESSIVE LOSS OF SIGNIFICANT DIGITS DURING DECOMPOSITION. WHEN A DECOMPOSED DIAGONAL IS LESS THAN THE BUILT-IN REDUCTION FACTOR TIMES THE ORIGINAL STIFFNESS MATRIX DIAGONAL, STAAD PRINTS A SINGULARITY NOTICE. THE BUILT-IN REDUCTION FACTOR IS 1.000E-09 THE ABOVE CONDITIONS COULD ALSO BE CAUSED BY VERY STIFF OR VERY WEAK ELEMENTS AS WELL AS TRUE SINGULARITIES ***WARNING - INSTABILITY AT JOINT 10 DIRECTION = FX PROBABLE CAUSE SINGULAR-ADDING WEAK SPRING K-MATRIX DIAG= 3.0792032E+00 L-MATRIX DIAG= 0.0000000E+00 EQN NO 43 ***NOTE - VERY WEAK SPRING ADDED FOR STABILITY ***WARNING - INSTABILITY AT JOINT 10 DIRECTION = FY PROBABLE CAUSE SINGULAR-ADDING WEAK SPRING K-MATRIX DIAG= 3.0792032E+00 L-MATRIX DIAG= 0.0000000E+00 EQN NO 44 ***NOTE - VERY WEAK SPRING ADDED FOR STABILITY ***WARNING - INSTABILITY AT JOINT 10 DIRECTION = FZ PROBABLE CAUSE SINGULAR-ADDING WEAK SPRING K-MATRIX DIAG= 1.2401584E+03 L-MATRIX DIAG= 0.0000000E+00 EQN NO 45 ***NOTE - VERY WEAK SPRING ADDED FOR STABILITY ***WARNING - INSTABILITY AT JOINT 10 DIRECTION = MX PROBABLE CAUSE SINGULAR-ADDING WEAK SPRING K-MATRIX DIAG= 2.5498595E+04 L-MATRIX DIAG= 1.4551915E-11 EQN NO 46

***NOTE - VERY WEAK SPRING ADDED FOR STABILITY ***WARNING - INSTABILITY AT JOINT 10 DIRECTION = MY PROBABLE CAUSE SINGULAR-ADDING WEAK SPRING K-MATRIX DIAG= 2.5498595E+04 L-MATRIX DIAG= 1.4551915E-11 EQN NO ***NOTE - VERY WEAK SPRING ADDED FOR STABILITY ***WARNING - INSTABILITY AT JOINT 10 DIRECTION = MZ PROBABLE CAUSE SINGULAR-ADDING WEAK SPRING K-MATRIX DIAG= 4.6276367E+03 L-MATRIX DIAG= 0.0000000E+00 EQN NO ***NOTE - VERY WEAK SPRING ADDED FOR STABILITY

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Making it as shown below, remove Problem with a degree of Freedom at joint 9 and 10 but not 8. This is because plates out considered pined at both top and Bottom. Adding Two Beams at Top connecting the loaded beam will solve the problem. The Beam may be defined as E having 1/100 of Actual and Density=0. However , warning will persist as ** WARNING ** A SOFT MATERIAL WITH (1.0 / 1.000E+02) TIMES THE STIFFNESS OF

This is just to inform the user.

CONCRETE ENTERED. PLEASE CHECK.