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 8-2: 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 8-3: 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 8-4: 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 8-5: 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 8-6: 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 8-7: 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 8-8: 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 8-9: 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 8-10: 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