Sample Problem : Timber Beam Design for Strength
A timber beam AB of span 5 m, width 100 mm and height 200 mm is to support three concentrated loads shown in the figure. The selected grade of timber has following material allowables ; τ_{all}=1 MPa and σ_{all}=10
MPa.
Calculate the maximum shear and normal stresses for the selected timber
beam for the given loading conditions.
Solution:
Step 1 : Write down input parameters (including material properties) which are
defined in the sample example.
INPUT PROPERTIES SUMMARY 
Parameter 
Symbol 
Value 
Unit 
Timber width 
b 
200 
mm 
Timber height 
H 
100 
mm 
Allowable shearing stress 
τ_{all} 
1 
MPa 
Allowable normal stress 
σ_{all} 
10 
MPa 
Type of Beam Design 
Simply supported beam
with multiple point loads 
Step 2 : Visit "Simply Supported Beam Deflection Calculation Example" page to
see calculation example for shear
force and bending moments. Calculate shear
forces and bending moments by using Simply Supported Beam Stress and Deflection Calculator as explained in the example.
Maximum shear forces and bending moments through the timber beam have been summarized below.
SHEAR FORCES AND BENDING MOMENTS 
Distance x 
Shear Force
(N) 
Bending Moment (Nm) 
0.5 
12676.5 
6323 
1.5 
2500 
8882 
See the sample calculation below for the first point given in the Step 2.

INPUT PARAMETERS 
Parameter 
Symbol 
Value 
Unit 
Structural Beam Height 
2c 
200 
mm 
Structural Beam Width 
b 
100 
Height y 
y 
100 
Shear Force 
V 
12676.5 
N 
Bending Moment 
M 
6323 
N*m 
OUTPUT PARAMETERS 
Parameter 
Symbol 
Value 
Unit 
Cross section area 
A 
20000 
mm^2 
First moment of area for the portion of the cross section above point y 
Q 
0 
mm^3 
Second moment of area 
I_{zz} 
66666668 
mm^4 
Normal stress at point y 
σ_{x} 
9.484 
MPa 
Shear stress at point y 
τ_{xy} 
0 
Von Mises stress at point y 
σ_{v} 
9.484 
Maximum normal stress 
σ_{max} 
9.484 
Maximum shear stress 
τ_{max} 
0.951 
Maximum Von Mises stress 
σ_{v_max} 
9.484 
Step 4 : Results for stress calculations are summarized in the following table.
RESULTS 
Distance x 
Shear Force
(N) 
Bending Moment (Nm) 
Max. Normal
Stress (MPa) 
Max. Shear
Stress (MPa) 
0.5 
12676.5 
6323 
9.484 
0.951 
1.5 
2500 
8882 
13.323 
0.188 
Summary
According to results, the design is not
safe for the given parameters and conditions. Maximum normal stress (13.323 MPa) is larger than allowable value (10 MPa) given in the problem.
A larger size timber beam shall be selected for a safe design.
The problem is fully solved with calculators and examples which are summarized as
follows.