1.4.2 Beam stress/displacement elements

ABAQUS Verification Manual

1.4.2 Beam stress/displacement elements

Product: ABAQUS/Standard

I. Load types: CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE, ROTA

Problem description

Model:

Length	15.0
Centrifugal axis of rotation	(0, 0, 1) through (7.5, 0, 0)
Gravity load vector	(1, 0, 0)
Beam section data:
Arbitrary (closed)	n = 4, A = (–.995, 1.49), B = (–.995, –1.49),
	= 0.01, C = (.995, –1.49), = 0.02,
	D = (.995, 1.49), = 0.01, E = (–.995, 1.49),
	= 0.02
Arbitrary (open)	n = 2, A = (0.0, 3.95), B = (0.0, 0.0), = 0.1,
	C = (3.95, 0.0), = 0.1
Box	a = 2.0, b = 3.0, = = 0.01, = = 0.02
Circle	r = 2.0
General	A = 12.566, = = 12.566, J = 25.133
Hexagonal	r = 2, t = 0.02
I-section	h = 2.4, l = 1.2, = 3.0, = 2.0, = = = 0.02
L-section	a = 4.0, b = 4.0, c = 0.1, d = 0.1
Pipe	r = 2.0, t = 0.2
Rectangular	a = 2.0, b = 3.0
Trapezoidal	a = 2.0, b = 3.0, c = 2.0, d = 1.5

Material:

Young's modulus	3 × 10⁶
Poisson's ratio	0.3
Density	0.16667
Coefficient of thermal expansion	0.0001

Initial conditions:

Initial temperature

ALL, –10.0

Results and discussion

The calculated reactions are in agreement with the applied loads.

Input files

Rectangular section

B21 element load tests:

CENT, CENTRIF, GRAV, PX, PY, P2, *TEMPERATURE.

P, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, P2, *TEMPERATURE.

P, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, P2, *TEMPERATURE.

P, *TEMPERATURE.

ROTA.

B21H element load tests:

CENT, CENTRIF, GRAV, PX, PY, P2, *TEMPERATURE.

P, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, P2, *TEMPERATURE.

P, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, P2, *TEMPERATURE.

P, *TEMPERATURE.

ROTA.

B22 element load tests:

CENT, CENTRIF, GRAV, PX, PY, P2, *TEMPERATURE.

P, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, P2, *TEMPERATURE.

P, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, P2, *TEMPERATURE.

P, *TEMPERATURE.

ROTA.

B22H element load tests:

CENT, CENTRIF, GRAV, PX, PY, P2, *TEMPERATURE.

P, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, P2, *TEMPERATURE.

P, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, P2, *TEMPERATURE.

P, *TEMPERATURE.

ROTA.

B23 element load tests:

CENT, CENTRIF, GRAV, PX, PY, P2, *TEMPERATURE.

P, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, P2, *TEMPERATURE.

P, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, P2, *TEMPERATURE.

P, *TEMPERATURE.

ROTA.

B23H element load tests:

CENT, CENTRIF, GRAV, PX, PY, P2, *TEMPERATURE.

P, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, P2, *TEMPERATURE.

P, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, P2, *TEMPERATURE.

P, *TEMPERATURE.

ROTA.

B31 element load tests:

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

ROTA.

B31H element load tests:

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

ROTA.

B32 element load tests:

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

ROTA.

B32H element load tests:

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

ROTA.

B33 element load tests:

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

ROTA.

B33H element load tests:

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

ROTA.

I-section

B22H element load tests:

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

P, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

P, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

P, *TEMPERATURE.

B31OS element load tests:

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

ROTA.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

B31OSH element load tests:

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

ROTA.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

B32H element load tests:

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

B32OS element load tests:

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

ROTA.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

B32OSH element load tests:

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

ROTA.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

Box section, arbitrary closed section

B22H element load tests:

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

P, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

P, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

P, *TEMPERATURE.

B32H element load tests:

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

Circular section

B22H element load tests:

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

P, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

P, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

P, *TEMPERATURE.

B32H element load tests:

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

General section

B22H element load tests:

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

P, *TEMPERATURE.

B32H element load test:

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

Hexagonal section

B22H element load tests:

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

P, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

P, *TEMPERATURE.

B32H element load tests:

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

L-section, arbitrary open section

B32H element load tests:

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

Pipe section

B22H element load tests:

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

P, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

P, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

P, *TEMPERATURE.

B32H element load tests:

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

Trapezoidal section

B22H element load tests:

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

P, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

P, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

P, *TEMPERATURE.

B32H element load tests:

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

CENT, CENTRIF, GRAV, PX, PY, PZ, P1, P2, *TEMPERATURE.

II. Load types: F1, F2

Problem description

Model:

Length	15.0
Rectangular section data	a = 2.0, b = 3.0
I-section data	h = 2.4, l = 1.2, = 3.0, = 2.0, = = = 0.2

Material:

Young's modulus	3 × 10⁶
Poisson's ratio	0.3

Results and discussion

The calculated reactions are in agreement with the applied loads.

Input files

Rectangular section

B21: F2.

B21H: F2.

B22: F2.

B22H: F2.

B23: F2.

B23H: F2.

B31: F1.

B31: F2.

B31H: F1.

B31H: F2.

B32: F1.

B32: F2.

B32H: F1.

B32H: F2.

B33: F1.

B33: F2.

B33H: F1.

B33H: F2.

I-section

B31OS: F1.

B31OS: F2.

B31OSH: F1.

B31OSH: F2.

B32OS: F1.

B32OS: F2.

B32OSH: F1.

B32OSH: F2.

III. Foundation types: FX, FY, FZ

Problem description

Model:

Length	10
Orientation	45° with horizontal axis
Pipe section data	r = 1.0, t = 0.05
I-section data	h = 2.4, l = 1.2, = 3.0, = 2.0, = = = 0.2

Material:

Young's modulus	30 × 10⁶
Poisson's ratio	0.3

Results and discussion

The calculated reactions are in agreement with the applied loads.

Input files

Pipe section

B21: FX, FY.

B21H: FX, FY.

B22: FX, FY.

B22H: FX, FY.

B23: FX, FY.

B23H: FX, FY.

B31: FX, FY, FZ.

B31H: FX, FY, FZ.

B32: FX, FY, FZ.

B32H: FX, FY, FZ.

B33: FX, FY, FZ.

B33H: FX, FY, FZ.

I-section

B31OS: FX, FY, FZ.

B31OSH: FX, FY, FZ.

B32OS: FX, FY, FZ.

B32OSH: FX, FY, FZ.

IV. Coriolis loading

Problem description

Model:

Pipe section data	r = 10.0, t = 1.0
I-section data	h = 2.4, l = 1.2, = 3.0, = 2.0, = = = 0.2
Axis of rotation	(0, 0, 1) through (0, 0, 0)

Material:

Young's modulus

30 × 10⁶

Initial conditions:

Initial velocity	ALL, 1, 10.0
	ALL, 2, 5.0
	ALL, 3, 2.0 (for 3-D beams)

Results and discussion

The calculated reactions are in agreement with the applied loads.

Input files

All elements are tested with the CORIO load.

Pipe section

B21 element.

B21H element.

B22 element.

B22H element.

B23 element.

B23H element.

B31 element.

B31H element.

B32 element.

B32H element.

B33 element.

B33H element.

I-section

B31OS element.

B31OSH element.

B32OS element.

B32OSH element.