Example:- Concrete masonry shear core

Accompanying this are three files named “STAGE_1.XSF”, “STAGE_2.XSF” and “COMPLETED.XSF”.  This is in metric units, large dimensions.


A concrete masonry shear core was constructed within an existing building. Generally the new masonry was fitted within the existing architecture. It was built in two stages. The second stage replaced an existing load bearing wall. The first stage was completed and loaded before that existing wall was demolished.
The two stages are shown in figure 1; the filled part being stage one and the outlined part stage two.

Figure 1 – Stages in the construction. Stage 1 in black, stage 2 in outline.

Standard hollow units that fit a 200 mm by 200 mm module and form a 190 mm thick wall were used.
To provide confinement and improve the ductility at each extremity 3 mm thick steel plates were laid in the mortar beds of the masonry. Each plate covered three modules.
The mortar, grout and the fabric of the masonry units are considered to be one material. However, as the properties of confined masonry differ from those of the unconfined masonry, each section of masonry wall with confining plates is described as a separate component.
The assumed stress-strain relationship of the masonry, both confined and unconfined, was as described in:

Priestley, M. J. N., Seismic Design of Concrete Masonry Shearwalls. ACI Journal, Proceedings, V.83, No 1, Jan-Feb 1986, pp 58-68.

The ultimate compressive strain in the unconfined masonry was assumed to be 2.5 x10-3 and that in the confined masonry 8.0 x10-3.

The vertical reinforcing was one 16 mm bar in every second flue. The steel modulus of elasticity was 200 GPa and yield stress 380 MPa.

The grouted masonry is expected to have had a drying shrinkage of 0.100 x10-3.

The centre of all gravity loads on the shear core was at the origin of the reference axes shown in Figure 2. That is at X = 300 mm, Y = 2900 mm on the axes adopted for the description of the components. All the load cases have these reference axes.

Figure 2 – Masonry core showing reference axis

The load taken by the first stage at the time the second stage was connected to it is assessed as 1.0 MN.

The instant of that connection is assumed to be when the grout in stage 2 set. Thus the loading and distortion of stage 2 at that instant is assumed to be all zeros.

This example investigates the behaviour of the completed shear core subjected to bending moments about the X axis in the negative direction. The reference angle is set at 180 degrees so that the references axis is parallel to the X axis but in the negative direction of the X axis. Such a bending moment would be caused by a horizontal force on the upper stories of the building tending to push the building in the direction of increasing Y.

The circumstances in the building are such that curvature of the shear core is not restrained. Thus, in this investigation, the bending moment about the references axis must be the only bending moment: the bending moment about the other axis must be zero.

The computation results set out in Table 1 describe the behavior of the cross-section under a gravity load of 900 kN, and bending moments about the X axis in the negative direction. The “Curvature references axis” and “Moment reference axis” columns in this table represented a moment-curvature relationship. The distortion information in this table represents only the “load case” distortion. It is suggested this is appropriate information to be used to assess the performance of a structures in an earthquake.

Table 1

Strain at origin Curvature references axis Curvature other axis Axial load Moment reference axis Moment other axis Load case
x10-3 x10-3/m x10-3/m kN MNm MNm
0.017 -0.006 0.027 -900 0.000 0.000 At rest
0.253 0.668 0.482 -900 1.468 0.000 1st yield
0.752 1.496 1.004 -900 2.081 -0.001 5th yield
1.118 2.057 1.330 -900 2.275 0.000 6th yield
1.878 3.142 1.898 -900 2.419 -0.002 7th yield
3.902 5.886 2.779 -900 2.518 0.001 8th yield
20.487 27.972 12.304 -900 2.554 0.002 Ultimate

Accompanying this are three files named “STAGE_1.XSF”, “STAGE_2.XSF” and “COMPLETED.XSF”. All three pertain to the same cross-section.

Step by step instructions are presented  in the download that start with the two files “STAGE_1.XSF” and “STAGE_2.XSF” and are intended to result in a file similar to “COMPLETED.XSF”. There is a sequence of computations that follows a chronological sequence of events in the construction of the shear core and results in a model of the completed shear core that is used to derive a moment – curvature relationship.

Descriptions of all the components in the two stages have been set up in the respective files together with descriptions of the materials. Also in “STAGE_1.XSF” the drying shrinkage of the stage 1 masonry has been taken into account and a Load case called “Stage 1 service” has been set up for the loading on stage 1 at the time it is connected to stage 2.

This example was described in a paper:

P. J. Thompson, “General Cross-section Analysis“, Transactions of the Institution of Professional Engineers New Zealand Vol 18 1/CE 1991.

However, this was written before several important conventions incorporated in the present version of the application had been adopted. In particular the approach to total distortion described in the present User’s Guide had not been adopted. The language in that paper could cause confusion in the present context.