##### Sample Problem : Timber Beam Deflection Calculations

A timber beam AB of span 3 m, width 200 mm and height 100 mm is to support three concentrated loads shown in the figure. Modulus of elasticity of selected class of timber is 8 GPa and the density of the timber is 600 kg/m3

Calculate the max. deflection, max. shear force, max. bending moment, mid-span deflection/slope and end reaction forces of the timber rectangular beam for the following loading conditions.

## 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 100 mm Timber height H 200 mm Timber length L 3000 mm Distance of x (Mid-span) x 1500 mm Elastic modulus of timber E 8 GPa Type of Beam Design Simply supported beam with multiple point loads

## Step 2 : Go to " Sectional Properties Calculator of Solid Rectangular Bar"  page to calculate second moment of area around x axis(Ixx)

 INPUT PARAMETERS Parameter Symbol Value Unit Height H 200 mm Width B 100 Length L 3000 Density p 600 kg/m3

 OUTPUT PARAMETERS Parameter Symbol Value Unit Cross section area A 20000 mm^2 Mass M 36 kg Second moment of area Ixx 66666668 mm^4 Second moment of area Iyy 16666667 Section modulus Sxx 666666.688 mm^3 Section modulus Syy 333333.344 Radius of gyration rx 57.735 mm Radius of gyration ry 28.868 CoG distance in x direction xcog 50 mm CoG distance in y direction ycog 100

## Step 4 : Calculation results of step 3 are as follows.

 No. Location Magnitude 1 0.5 m 10 kN 2 1.5 m 5 kN 3 2.5 m 10 kN
CONCENTRATED MOMENTS
 No. Location Magnitude
 No. Start Location Magnitude End Location Magnitude 1 0 m 117.7 N/m 3 m 117.7 N/m
RESULTS
Parameter Symbol Value Unit
Reaction Force 1  R1 12676.5 N
Reaction Force 2 R2 12676.5
Transverse Shear Force
@ distance x
Vx 2500.0
Maximum Transverse
Shear Force
Vmax 12676.5
Moment @ distance x Mx 8882.4 N*m
Maximum Moment Mmax 8882.4
Slope 1  θ1 -0.988 degree
Slope 2 θ2 0.988
Slope
@ distance x
θx 0.000
Maximum Slope θmax -0.988
Deflection @ distance x yx -15.662 mm
Maximum Deflection ymax -15.662
Bending Stress @ distance x σx 6.7 MPa
Maximum Bending Stress σmax 6.7

##### Summary

Max. deflection, max. shear force, max. bending moment, mid-span deflection/slope and end reaction forces of the timber rectangular beam have been calculated with the usage of the following calculators.

 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.