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 ; τall=1 MPa and σall=10 MPa.

Calculate the maximum shear and normal stresses for the selected timber beam for the given loading conditions.

Timber Beam Design For Strength Example

Solution:

Step 1 : Write down input parameters (including material properties) which are defined in the sample example.

INPUT PROPERTIES SUMMARY
Parameter Value
Timber width [b] 200 mm
Timber height [H] 100 mm
Allowable shearing stress [τall] 1 MPa
Allowable normal stress [σall] 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



Step 3 : Visit "Rectangular Beam Design For Strength"  page to calculate maximum shear and normal stresses.

See the sample calculation below for the first point given in the Step 2.

Sectional properties of solid rectangle
INPUT PARAMETERS
Parameter Value
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 Value
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 [Izz] 66666668 mm^4
Normal stress at point y [σx] 9.484 MPa
Shear stress at point y [τxy] 0
Von Mises stress at point y [σv] 9.484
Maximum normal stress [σmax] 9.484
Maximum shear stress [τmax] 0.951
Maximum Von Mises stress [σv_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.


Calculator Usage
Solid Rectangular Bar - Sectional Properties Calculator To calculate sectional properties of rectangular solid bar.
Simply Supported Beam Stress and Deflection Calculator To calculate forces, moments, stresses, deflections and slopes in a simply supported beam for multiple point loads, distributed loads and concentrated moments.
Simply Supported Beam Deflection Calculation Example An example on calculation of max. deflection, max. shear force, max. bending moment and mid-span slope/deflection of a simply supported beam under multiple point loads and a distributed load.