Ahsan Sattar, PhDSenior Engineer, NESPAKahsansattar@hotmail.com

Section cut in SAP2000How is the plane of the section cut defined when drawn in a 3D view?Expanded Question:When a section cut is drawn in a 3D view, only the X and Y coordinates are provided. How is the section-cut plane defined?Answer:When using the Draw > Draw Section Cut command, forces are reported in thesection-cutcoordinate system which is defined by three axes (1,2,Z) as follows: Section-cut 1 axis is located within the plane parallel to the global X-Y plane, and rotates counterclockwise from the global X axis according to the user-defined parameter Angle (X to 1). Section-cut 2 axis is also located within the plane parallel to the global X-Y plane, though it is oriented 90 counterclockwise from the section-cut 1 axis. Section-cut Z axis is parallel to the global Z axis.Integrated forces are reported either on the left or right side of the section cut, according to the right-hand rule. Take, for example, a section cut drawn from left to right along the horizontal plane within a X-Z view. Integrated forces on the left side represent behavior above the section cut, while those on the right side, below. Using the right-hand rule, these forces are expressed in the section-cut coordinate system (1,2,Z).Why are section-cut integrated forces shown in 1,2,Z and not 1,2,3 directions?Answer:For section cuts drawn within the graphical user interface, the section-cut 3 axis is always parallel to the global Z axis, therefore integrated forces are shown in 1,2,Z directions since this notation is more precise.

Why is the magnitude of integrated forces different for the left and right sides?Expanded Question:According to equilibrium, should not the magnitude of integrated forces be equivalent for both left and right sides?Answer:Section-cut forces may be different on either side of asection cutbecause they are based on joint forces which occur in the global system. Globally, these forces are in equilibrium, but their relation to a section cut is arbitrary and does not necessarily serve the function and conditions of a free-body diagram. As an example, consider a section cut located in the middle of a cantilever beam modeled by a single frame element and loaded by its self-weight only. The results on the side of the section cut that includes the fixed end will represent the beam reactions, while the results on the side of the section cut that includes the free joint will be zero.

Example of Section cut

Expanded Question:Consider a cantilever beam made of solid elements. Figure below shows the beam with the unit (1lb) load at the end of the beam. The global axes are also displayed for reference. (Note :- Example 5-002 of the verification manual of SAP2000 v 14.1.0 is used here)Hand calculations shows Max. shear force = 1lbMax. Bending moment at support = 1 x 6 = 6 lb-inStress = 6 x 0.1 / (0.1 x 0.23 /12) = 9000 psi

Figure 1:- FEM model of cantilever beam with unit load at the tip.Figure 2 shows the longitudinal stresses in the beam. The maximum stress of 9000psi is shown near the support.

Figure 2:- Longitudinal stresses in the beam subjected to unit load in z-direction at its tip.Draw a section cut near the support to determine the bending moment keeping in mind the orientation of axes of section cut as explained above.Display the beam in xz-plan to view draw the section cut conveniently. Zoom near the support as the forces are desired near the support. Draw a section cut line near the support. Now adjust the coordinates of the start and end of the line to adjust the line at 0.05 from the support and is parallel to the z-axis. The location of the resultant is to be adjusted to the desired location. We need to output forces at mid height of the section so that bending moment is integrated about the mid of the section. Adjust the X of resultant to desired location. For this beam the width is 0.1, so put 0.05 to be at mid of the width. Adjust Z to mid height of section (Although in this example it will not affect the results). The most important here is to adjust the angle. The Angle (X to 1) is the angle by which the 1-axis of the section cut is to be rotated counterclockwise from the global x-axis. The 1-axis of section cut is always in the global xy-plane. The 2-axis of the section cut is 90 CCW from the 1-axis.For this example, if angle for resultant is put as zero, the 1 axis will be in the direction of global x-axis. The 2 axis will be into the paper. Hence the major bending moment will be about the 2 axis. The major shear force will be in the Z direction. The results are displayed in figure 3.

Figure 3: Section cut output and explanation