MasterFrame Coordinate System

Within MasterFrame, loadings and supports are defined relative to the global axes coordinate system. End releases and partial end fixities are defined relative to the member local axes. The axes systems are as follows: -

The system of co-ordinates used in defining the structure as a whole. The Global X-axis is horizontal and acts positively towards the right. The Global Y-axis is vertical and acts positively upward. The Global Z-axis is perpendicular to the XY plane and acts positively into the screen.

The system of co-ordinates is used to define the signs of the internal forces and any loads acting normal to the member. It is sometimes known as the member system of co-ordinates.

The local y-axis is obtained by a 90-degree anti-clockwise rotation of the local x-axis.

The local z-axis acts perpendicular to the local XY plane and is found by rotating 90 degrees clockwise about the local X axis.

Plane Frame Grillage

The Relationships Between the Global and the Local Systems of Co-ordinates

Please always use the load diagram to confirm the direction of normal to member loads.

The diagram above illustrates the relationships between the Global and the Local systems of co-ordinates for plane and grillage frames.

The distances used in defining load positions, haunch dimension and/or design check requirements are measured along the slope of the member from node n1.

In plane frames, these include the nodal displacements in the Global X and Y directions, and the nodal rotation about the Z axis. In grillages, the nodal deflections include the nodal rotation about the X and Z axes along with the vertical displacement in the Y direction. Please note that for an East-West member the X rotation is a torsional rotation and the Z rotation is a bending rotation

Plane Frame Grillage

The Sign Convention for the Nodal Deflections

In addition to the values of the Axial force, the Shear force and the Bending moment at the ends of each member, the value and position of the maximum Bending moment, and the value and position of the maximum member deflection are also printed.

In the output, the maximum member deflection is defined as the maximum deflection resulting from the local curvature of the member, measured in relation to the straight line connecting the new nodal positions. This value is generally more relevant than the absolute deflection, particularly in the case of a multi-storey structure. The following diagram illustrates the significance and the sign convention used in conjunction with the maximum member deflection.

The Maximum Member Deflection (Plane Frames)

The Sign Convention (Plane Frames)

In plane and space frames, a positive value for axial force indicates compression, and a negative value indicates tension. The standard convention is used for the shear force and the bending moment. However, it should be noted that the latter relates to the orientation of the member, as shown in the diagram above.

In grillages and space frames, a positive torsional moment indicates an anti-clockwise torsion as seen when looking down the member from the smaller node number to the larger node number.

The support reactions are based on the out of balance forces at each joint in the model. The sign convention for the support reactions is illustrated in the figure below. This shows the positive directions for the six global degrees of freedom.

With the Pin-Jointed Frame Analysis, the output is considerably more compact than in the case of the Rigid Frame Analysis. The nodal deflections in the Global X, Y and Z directions are given using the same sign convention as with rigid frame, but here only the axial force in each member, together with the axial stress, the length and the type of member are printed.

As before, a positive value of axial force indicates compression, and a negative value indicates tension. In all other respects the output is similar to that obtained in the case of a Rigid Frame Analysis.