Bending and Stretching of an Elastic L-Beam

geometry

b (mm)

80

h (mm)

106.914

e

1

(mm)

6

e

2

(mm)

8

loading

N (kN)

10

(N)

x

(mm)

-20

(N)

y

(mm)

-20

parameters of σ plot

place

scale

computed characteristics of the section

A	S x	S y	(G) x	(G) y
2 cm	3 cm	3 cm	mm	mm
12.3	29.28	-21.96	-17.8	23.7

I xx	I yy	I xy	α
4 cm	4 cm	4 cm	°
136.73	76.47	-60.91	-31.8

I ξξ	I ηη	ρ ξ	ρ η
4 cm	4 cm	mm	mm
174.55	38.65	17.7	37.6

β	γ	x a	y a
°	°	mm	mm
13.2	-109.4	15.7	70.8

σ 1	σ 2	σ 3	σ 4	σ 5	σ 6
MPa	MPa	MPa	MPa	MPa	MPa
24.4	20.	5.6	2.6	-15.6	-17.

The normal stresses (a.k.a. longitudinal stresses) in an elastic beam with an L-shaped cross section loaded by bending moments and by a normal force are computed by the generalized Navier's formula.

This Demonstration shows the central ellipse of inertia and the principal inertia axes of the cross section, displaying the axis of flexure (in red) and the neutral axis (in blue) and plotting the stress diagram.