VM-WB-MECH-023

VM-WB-MECH-023
Curved Beam Assembly with Multiple Loads

Overview

Reference:	Any basic Strength of Materials book
Solver(s):	Ansys Mechanical
Analysis Type(s):	Linear Static Structural Analysis
Element Type(s):	Beam

Test Case

An assembly of two curved beams, each having an included angle of 45°, has a square cross-section. It is fixed at one end and at the free end a Force F and a Moment M are applied. Also, a UDL of "w " N / mm is applied on both the beams. Use a global element size of 30 mm to get accurate results. See the figure below for details.

Find the deformation of the free end in the y direction.

Figure 26: Schematic

Equivalent Loading:

Material Properties

Geometric Properties

Beam 1:

E₁ = 1.1e5 MPa

ν₁ = 0

ρ₁ = 8.3e-6 kg/mm³

Beam 2:

E₂ = 2e5 MPa

ν₂ = 0

ρ₂ = 7.85e-6 kg/mm³

For each beam:

Cross-section = 10 mm x 10 mm

Radius r = 105 mm

Included angle = 45°

Force F = -1000 N (y direction)

Moment M = -10000 Nmm (about z-axis)

UDL w = -5 N/mm (y direction) on both beams

This UDL is applied as an edge force on each beam with magnitude = -5 (2 x 3.14 x 105) / 8 = -412.334 N

Analysis

The deflection in the y direction is in the direction of the applied force F and is given by:

where:

δ = deflection at free end in the y direction

I = moment of inertia of the cross-section of both beams

Results Comparison

Results	Target	Mechanical	Error (%)
Minimum Y Deformation (mm)	-8.416664	-8.4688	0.619