Geoff's Woodwork 

 
 
 for Students of Woodwork                                                       

Using timber structurally

calculating strength properties

modulus of elasticity

useful facts and data

weights for common books

Using timber structurally

The table below gives the approximate weight of various sized books per 500 mm run.   It does not give the material or thickness, etc. of the required board.  For this, you should calculate using the materials MoE (modulus of elasticity) and the various bending formulas. You may obtain these and a good working explanation from Bruce Hoadleys book "Understanding Wood".  Another excellent book about shelf loads and other formula is the "Woodworkers Essential" by Ken Horner.   I have included some formula and calculations collected from various sources over my teaching and learning career.   I must confess that I am not entirely happy using raw data or formula without carrying out a practical test of the likely loads on a mock up using the proposed material and spans.   The formulas do not include a margin for safety and I would reduce the predicted spans to give a degree of tolerance especially those calculated with fixed ends.   A batten added to the front and the rear of the shelf will provide a greater load potential.

To get an idea of the safe loading you could always preload your shelf with an approximate weight that you intend to load.   Even if it is only the proposed board set out between a couple of supports.   Weigh a single brick (or similar common unit) and then load the board with them until the board starts to dip.    If you multiply the single units weight by the total number of units that it safely took  (with a safety allowance) you will have an idea what weight the given board (material, span, thickness and depth) will take.   You may then modify the span, thickness, etc. accordingly before committing yourself.  In my calculations I use a deflection of an eighth of an inch (about 2.54 mm).  This is a tolerable deflection but the amount should be changed to that required for the job.     When designing shelves for bookcases and similar loading start at a finished thickness of one inch (25mm) anything less calls for quite short spans.

It is surprising how heavy books and other ornaments are.   You should err on shorter shelving rather than the longer variety unless you are confident that the thickness of your chosen board can take it.   I note that many designers and writers are loathe to quote loading tables nowadays.   Failure could be expensive.    Remember, if you make someone a piece of furniture and it fails and someone gets injured it is you the designer who is responsible.   As the manufacturer you are responsible for any production errors and failures.  Try to obtain the customers written plans and specifications but use your good judgment before production and if you are not sure, check.

Please be careful when making bookcases and shelving or anything that may take a lot of weight.   If in doubt ask an expert.  Although in my opinion, it is difficult to get one to commit themselves.  Remember, make practical tests before you use such tables and formulaes.  They are a good starting guide but not final proof!  

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Calculating Strength properties of timber

These formulas do not include a safe operating margin. Users should satisfy themselves that the formula is correct for their application and carry out physical checks to confirm safety.

1.     Uniformly distributed  load, with supported ends such as adjustable shelving, etc

   s =       (5 x F x L )  (384 x E x I)  

L =    v ((384 x s x E x I) (5 x F))

I =      b x h    12

Where:

s  =  deflection

F  =  Force in Newtons

L  =  Span

E  =  Modulus of Elasticity in N/mm

I  =  Moment of inertia

b  =  breadth (depth) in mm

h  =  height (thickness) in mm

2.  Uniformly distributed  load, with fixed ends i.e. secured in housings or dado:

s =       (F x L )    (384 x E x I)

L =    v ((384 x s x E x I) F)

I =      (b x h)    12

Note when the ends are securely fixed such as in a glued housings or dado the increase in load capacity.   To obtain the advantage of these spans the ends must be held extremely stiff because any movement will reduce the load potential.   I doubt if the full advantage would be obtained using standard timber shelving and normal jointing methods.  However it is included for comparison purposes and to demonstrate the obvious advantage of fixing the ends securely as possible.

Summary of methods to increase load capacity:

a.       Ends firmly fixed into supports.

b.      Wider the board - the amount of load may increase by twice the load by increasing twice the width.

c.      Thicker the board - the amount of sag in the board may decreased by a factor of eight by doubling the thickness.

d.       Shorter the span  - on the other hand by doubling the supported span the amount of sag increases by a factor of 8.

By scrutiny of the E values below you will see the stronger timbers to use and the obvious weakness of using man-made boards such as plywood and MDF despite its wide use in the shelving business.

If a certain span is required that would otherwise would sag due to its thickness the remedy is to provide dividers to decrease the span or increase the load capability by using a wider board.

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Modulus of Elasticity. E value

Users should obtain their specific data from the manufactures or suppliers specification sheets.

The data supplied below is some that the author has collected from various sources and is quoted only below to show the range available.  No apologies are made for the wide values shown against some timbers.  This information is collated from sources such as technical publications, data sheets from TRADA, and BRE.(see for web sites)   The wider variations are generally for differing characteristics between similar species, their country of origin and always, the local conditions that the tree grew in.   You should obtain E values from your supplier and when using the boards in a critical situation take physical checks to ensure the material is up to the stability for the use you are putting it.   There are further factors that affect the strength of timber such as the temperature, the amount of moisture, the grain direction and slope, the physical defects such as knots, shakes, splits, mature or juvenile wood, etc.   All this leads to the absolute need to provide practical tests before using boards to carry weight.

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Material                 Density  = Kg/m          E  in N/mm2

Ash European

689

11,900

Balsa

176

3200

Birch European

670

13300

Beech European

673

12600

Cedar UK

417

5400

Cherry USA

580

10,200

Chestnut sweet

560

8,200

Douglas Fir Canada

545

12700

Hemlock Canada

465

10400

Iroko

655

9,400

 

Larch European

545

9900

Keruing/Luan spp.

641-849

13,700  - 17600

Mahogany var. spp

495-850

7,800 10,600

Meranti/

481

10500

Oak European

689

10,100

Parano Pine

529

10400

Spruce sitka Canada

384

8100

Sapele

673

11,700

Scots Pine

513

10000

Sycamore European

561

9400

Teak

641

10000

Utile

660

10800

Walnut African

545

9,200

Western Red Cedar

368

7000

Whitewood European

417

10200

MDF HD 17-19 mm   3,450 5,000
MDF Std  18 19 mm   3,000
Chipboard 12 19 mm   1,600 3,400

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Useful facts and data

When gathering data for your calculations you will find the tables will reveal the material you are looking for but often in the wrong unit.  The table below gives some conversion factors that might be useful to convert the information to the correct format.

Stress (s)

s = load/area    (MN/m or lb/inch or psi)

Strain  (e)

e = amount of stretch/original length (no units)

Youngs modulus (E)

E = stress/strain = s/e   (N/mn)

 

 

density

= Wt Kg / vol cm

 mass

= volume x density 

specific gravity (sg)

= Kg/m

1 psi = 0.00685 MN/m
  = 0.07 Kg/cm
1 kg/cm = 0.098 MN/m
  = 14.2 psi
   
1 MN/m = 10.2 Kg/cm = 146 psi
KN/mm = 1000N/mm
N/mm = 1MPa
  = 1 N/m x 10^6
KN/mm = 1GPa
  = 1 N/m x 10^9

1 Pascal

= 1 N/m

1Kg force = 9.8N
1 m =  1000000 cm
  =  1000000000 mm
   
1 cc (  mass of 1 gram) = 1 millilitres or 1ml
   = 0.001 Litres
  = 0.000001 m
1 Litre = volume of 1 Kg of pure water @ 40C
   = 1000 cc = 100 cl
  = 1000 ml 
  = 1000 cm
1 m = 1000 Litres
1 grain = 1/7000 lb
1 Lb/foot  = 4.88 Kg/m
1 lb/Cu.Ft = 16.0185 Kg/m
1 Lb/Cu.Inch = 27679.90  Kg/m
   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Weight of books  

The average weight of standard books per 500 mm run:

Small paperback                                      8  X  5    inches       10.29 Kg  

Small modern compact paper backs        8    X  6 inches            15.7 Kg

Small hardback older book                      9  X  6 inches                 11.84 Kg   

Medium hardback book                           10  X  7 inches           17.4  Kg    

Large hardback book                                12  X  9   inches          37.2 Kg  

I have been asked a number of times the source of the book weights.
The weights are purely average based on Practical Observations. 
I took say 4 or 5 books each of the same sizes,  weighed them and measured the total thickness of the bundle in mm. 
The weight was divided by the total thickness and multiplied by 500.
Therefore the 'weight per 500mm run'  is purely as a guide to how heavy books of given sizes represent a shelf
of span 500 mm loaded with books to fill the shelf.
I did this to each size range of book.  Now you may well have a heavier paper and book boards so CHECK!
I recommend that you carry out and check  the exercise yourself if you are going to do design work.
   

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text and grafics Geoff Malthouse


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revised and uploaded 3rd March 2010