analysis of confined masonry part 2
TRANSCRIPT
Analysis of Confined Masonry Buildings: Part 2
Juan José Pérez-Gavilán EApplied Mechanics
Institute of Engineering, UNAM
Short Course on Seismic Design of Reinforced and Confined Masonry Buildings
February 17-21, 2014, IIT Gandhinagar, India
Wide columnEffective width
|
Modelling parapets
hinge
Modelling in 3D
Modelling example
Axis 1
Axis 2
Axis A
Axis B
Axis C
Sections
Final model
Finite elements
FE- Axis 1
FE – Axis 2
FE- Axis 3
FE – Axes A and C
FE – Axes B
Floor
Diaphragm can be modelled as rigid in its plane Using SAP2000, select all the nodes at the level
floor, then use “Constraint, Diaphragm” option. Reduces all degrees of freedom in the plane of
the floor to just 3: two displacements in the plane of the floor and a rotation about an axis that is perpendicular to the plane.
Out of plane degrees of freedom are preserved in each node.
Numerical experiments
Control sections
Reference model
M1-FR1 M1-FR2
M1-FR3 M1-FR4
For the completeset of numericalexperiments seeTaveras 2008
Rigid elementsshown with thickerlines
Shear force
Control section
Shear
Large error show up using model FR-3 Model M1-FR1 seems to be more consistent. All models give good results for total shear in
sections S1 and S2 (M1-FR4 the worst) For the wall segments around the windows
larger errors were found. Left segments underestimated the shear force
and the right segments overestimate it
Moment
Control section
Moment
Large errors were found using model FR-3. This result is attributed to the fact that the model does not take into account the first parapet connected to the foundation (as is currently in the NTCM)
Model M-FR4 seems to be the more consistent, followed by M-FR1
All models give good results for complete sections S1 and S2, however, for the control sections in the wall segments to the side of the windows considerable errors were found
Axial force
Control section
New recommendation
The recommendation takes into account numerical experiments for coupling wallsnot shown in the preceding slides
Sections
Wall division for modelling
G=0.4 E G=0.2 EFixed 1.632 1.155cantilever 1.915 1.354
Dividing is ok if L/H > 1.4
H/L having and error equal to 20%
𝛽=1 𝛽=0
33
Finiteelements
M1-EF1 M1-EF2
M1-EF3 M1-EF4
Tie-columns are included as frame elements
The frame elements should follow the discretization of the grid
Same effective with as in wide columns models should be used
Shear force
More consistent than FR models
Control section
Shear
Errors were up to 12%, smaller than with FR models
Model M1-EF2 seems to be more consistent Finite element models appear more robust as
they can recover the shear forces in the wall segments at both sides of the windows.
Moment
Control section
Moment
Errors less than 35% were obtained with all models In all control sections the model that produced the
best results is the one with coarsest gird (M1-EF1) It seems that because the frame and finite
elements are not compatible, regarding the rotational degrees of freedom, an error is always included, that may grow as the grid is subdivided
When continually subdividing the mesh eventually there is convergence on displacements, but to a wrong value
Axial force
Control section
Axial force
Axial force appears to be very difficult to recover accurately, specially in the wall segments at each side of the windows
In all control sections the model that produced the best results is the one with coarsest gird (M1-EF1)
40
Displacements
Displacements (cm)
Hei
ght (
m)
FR3, which do not consider the parapet of first floor overestimates the displacements Considerably. FR4 are quite good, and with FE models are, in general, larger than expected
Summary/comments Wide column models (FR) cannot deal with complex force transmission
they do well for uniform frames and walls with no windows Not shown above, however by enforcing the flat section in walls in 3D
sometimes gives unexpected effects, for example when modelling “T” shaped walls, the effect of the flange is exaggerated when considering analysis in the direction of the web. An effective flange width should be considered but FR models cant. FE models in the other hand are much more flexible and do not impose artificial hypothesis
Tie-columns should be modelled. In case tie-columns are not included in the model, one may expect a
similar distributions of forces in the walls, however, the displacements are much larger and the period is increased, consequently the design will be conservative, as larger period usually means larger shear forces, for masonry structures.
Parapets play an important role on the behaviour of a frame with windows, they should be modelled, specially the one of the first floor.
FE vs FR
Finite element models– Are more robust– The model preparation is time consuming and error
prone.– It take much time to recover the element forces for the
design Wide column models– Give good results for shear and are less accurate for
moment and axial forces, specially around windows– Models are relatively simple to prepare– Recovering of the element forces is immediate
Questions?