Shell Element Internal Forces Stresses Output Convention
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Shell Element Internal Forces/Stresses Output O utput Convention The six faces of a shell element are defined as the positive 1 face, negative 1 face, positive 2 face, negative 2 face, positive 3 face and negative 3 face as shown in the figure below. In this definition the numbers 1, 2 and 3 correspond to the local axes of the shell element. The positive 1 face of the element is the face that is perpendicular to the 1-axis of the element whose outward normal (pointing away from the element) is in the positive 1-axis direction. The negative 1 face of the element is a face that is perpendicular to the 1-axis of the element whose outward normal (pointing away from the element) is in the negative 1-axis direction. The other faces have similar definitions.
Note that the positive 3 face is sometimes called the top of the shell element in SAP2000, particularly in the output, and the negative 3 face is called the bottom of the shell element. Shell Element Internal Forces Shell Element Internal Stresses The basic shell element stresses are identified as S11, S22, S12, S13, and S23. An S21 might also be expected, but S21 is always equal to S12, so it is not actually necessary to report S21. Sij stresses (where i can be equal to 1 or 2 and j can be equal to 1, 2 or 3) are stresses that occur on face i of an element in direction j. Direction j refers to the local axis direction of the shell element. Thus S11 stresses occur on face 1 of the element (perpendicular to the local 1 axis) and are acting in the direction parallel to the local 1 axis (that is, the stresses act normal to face 1). As another example, S12 stresses occur on face 1 of the element (perpendicular to the local 1 axis) and are acting in the direction parallel to the local 2 axis (that is, the stresses act parallel to face 1, like shearing stresses). The figure below shows examples of each of these basic types of shell stresses. SAP2000 reports internal stresses for shell elements at the four corner points of the appropriate face of the element. For example, refer to Figure a below. On the positive 1 face internal stresses are reported by SAP2000 at points A, B, C and D.
Shell Element Internal Forces Stresses Output Convention
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Shell internal stresses are reported for both the top and the bottom of the shell element. The top and bottom of the element are defined relative to the local 3-axis of the element. The positive 3-axis side of the element is considered to be the top of the element. Thus in Figure a above, internal stresses at the top of the element include stresses at the joints labeled A and C and internal stresses at the bottom of the element include stresses at the joints labeled B and D. The Figure below clearly illustrates the points where SAP2000 reports the shell element internal stress values.
Shell Element Internal Forces Stresses Output Convention
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The transverse shear stresses calculated by SAP2000 (S13 and S23) are average values. The actual transverse shear stress distribution is approximately parabolic; it is zero at the top and bottom surfaces and has its maximum or minimum value at the midsurface of the element. SAP2000 reports the average transverse shear value. An approximation to the maximum (or minimum) transverse shear stress would be 1.5 times the average shear stress. The figure below illustrates the positive directions for shell element internal stresses S11, S22, S12, S13 and S23. Also shown are the positive directions for the principal stresses, S-Max and S-Min, and the positive directions for the maximum transverse shear stresses, S-Max-V.
Shell Element Internal Forces Stresses Output Convention
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For values of S13 and S23 at any angle, the maximum transverse shear stress, S-MaxV, can be calculated from:
See Also: Sign Convention
