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

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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)

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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?