Тест 1.16 A beam restrained at the ends, loaded with a uniformly distributed load

Verification of the LIRA-FEM software / Тест 1.16 A beam restrained at the ends, loaded with a uniformly distributed load / Pisarenko G.S, Yakovlev A.P., Matveev V.V. Handbook of Strength of Materials. - Kiev : Learning Opinion, 1988.

Linear static problems for rod systems, plates and shells, three-dimensional problems

Analytical solution: Pisarenko G.S., Yakovlev A.P., Matveev V.V. Reference Book on Strength of Materials. - Kiev: Scientific Opinion, 1988.

Task wording: The beam pinched at the ends is loaded by a uniformly distributed load q. Determine the maximum lateral displacement w.

Input data:

E = 3.0·10⁷Па	- modulus of elasticity,
μ = 0.25	- Poisson's ratio,
l = 2.4 м	- girder length;
b = 0.2 м	- beam section width;
h = 0.3 м	- beam section height;
q=10 кН/м	- load value.

Calculation results:

The analytical solution of the deflection in the center of the beam can be calculated by the following formula (Pisarenko G.S., Yakovlev A.P., Matveev V.V. Handbook of Strength of Materials. - Kiev: Scientific Opinion, 1988).

Note:Rod model FE10 - universal spatial Rod FE (without taking into account cross-slip deformations (Fig.1, Table 1), and with consideration of shear (Fig.2)); plate model: FE 21 - rectangular FE of a flat problem (beam-wall) (Fig.1, Table 2); FE 28 - rectangular FE of a flat problem (beam-wall) with intermediate units on the sides (Fig.2)

CALCULATION RESULTS:

Table 1

The desired value	Analytical solution	Calculation results (LIRA-FEM FE) 10)	Uncertainty,%
Transverse displacement in the middle of the beam span, mm	-0.064	-0.064	0.00

Table 2

The desired value	FE grid with dimensions	Analytical solution	Calculation results (LIRA-FEM FE 21)	Uncertainty,%
Transverse displacement in the middle of the beam span, mm	2х6	-0.064	-0.0099	84.53
	4х6		-0.0284	55.62
	8х6		-0.0530	17.19
	16х6		-0.0679	6.09

Рис. 1. Перемещение z, мм в центре балки (без учета деформаций поперечного сдвига)

Fig. 2. Displacement z, mm in the center of the beam (c accounting for transverse shear deformations)

Preview image: Array

Note: Rod model FE 10 - universal spatial Rod FE (without taking into account cross-slip deformations (Fig.1, Table 1), and with consideration of shear (Fig.2)); plate model: FE 21 - rectangular BE of a flat problem (beam-wall) (Fig.1, Table 2); FE 28 - rectangular BE of a flat problem (beam-wall) with intermediate units on the sides (Fig.2)

FILES

Тест 1.16 A beam restrained at the ends, loaded with a uniformly distributed load

Comments

Follow us