Common Cross Sections

Common Cross Sections

The cross-section data for the common cross sections can be computed internally in COMSOL Multiphysics. In this section, the expressions used are summarized.


	Beam Cross Section

Rectangular Section

Figure 8-7: Geometry of a rectangular cross section. The diagram also displays in COMSOL Multiphysics when this option is selected.

Table 8-2: Rectangular Section Constants.
Property	expression	Remarks
A
Izz
ez	0
μy	1.5
κy	5/6
Iyy
ey	0
μz	1.5
κz	5/6
J		q= min(hy/hz, hz/hy)
Wt		q= min(hy/hz, hz/hy)
p1
p2
p3
p4
re

Figure 8-8: Geometry of a box shaped cross section. The diagram also displays in COMSOL Multiphysics when this option is selected.

Table 8-3: Box Section Constants.
Property	expression	Remarks
A
Izz
ez	0
μy
κy
Iyy
ey	0
μz
κz
J		Thin-walled approximation
Wt		Thin-walled approximation
p1
p2
p3
p4
re

Circular Section

Figure 8-9: Geometry of a circular cross section. The diagram also displays in COMSOL Multiphysics when this option is selected.

Table 8-4: Circular Section Constants.
Property	expression	Remarks
A
Izz
ez	0
μy
κy	0.9
Iyy
ey	0
μz	μy
κz	κy
J
Wt
p1
p2
p3
p4
re

Figure 8-10: Geometry of a pipe cross section. The diagram also displays in COMSOL Multiphysics when this option is selected.

Table 8-5: Pipe Section Constants.
Property	Formula	Remarks
A
Izz
ez	0
μy
κy
Iyy
ey	0
μz	μy
κz	κy
J
Wt
p1
p2
p3
p4
re

H-Profile Section

Figure 8-11: Geometry of an H-profile cross section. The diagram also displays in COMSOL Multiphysics when this option is selected.

Table 8-6: H-Profile Section Constants.
Property	expression	Remarks
A
Izz
ez	0
μy
κy
Iyy
ey	0
μz
κz
J		Thin-walled approximation
Wt		Thin-walled approximation
p1
p2
p3
p4
re

U-Profile Section

Figure 8-12: Geometry of a U-profile cross section. Also displays in COMSOL Multiphysics when this option is selected.

Table 8-7: U-profile Section Constants.
Property	expression	Remarks
A
Izz
zCG
ez
μy
κy
Iyy
ey	0
μz
κz
J		Thin-walled approximation
Wt		Thin-walled approximation
p1
p2
p3
p4
re

T-Profile Section

Figure 8-13: Geometry of a T-profile cross section. Also displays in COMSOL Multiphysics when this option is selected.

Table 8-8: T-profile Section Constants.
Property	expression	Remarks
A
yCG
Izz
ez	0
μy
κy
Iyy
ey
μz
κz
J		Thin-walled approximation
Wt		Thin-walled approximation
p1
p2
p3
p3
re

C-Profile Section

Figure 8-14: Geometry of a C-profile cross section. Also displays in COMSOL Multiphysics when this option is selected.

Table 8-9: C-profile Section Constants.
Property	expression	Remarks
A		q
Izz		q
zCG		q
ez		See below the table
μy		q
κy		q
Iyy
ey	0
μz
κz
J		Thin-walled approximation
Wt		Thin-walled approximation
p1
p2
p3
p4
re

The expression for the shear center offset is valid only for the case when the thickness is constant, that is

Figure 8-15: Geometry of a Hat cross section. Also displays in COMSOL Multiphysics when this option is selected.

Table 8-10: Hat Section Constants.
Property	expression	Remarks
A
Izz
zCG
ez		See below the table
μy
κy
Iyy
ey	0
μz
κz
J		Thin-walled approximation
Wt		Thin-walled approximation
p1
p2
p3
p4
re

The expression for the shear center offset is valid only for the case when the thickness is constant, that is