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 Hoadley’s 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 them. 

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

   σ =       (5 x F x L ³) ÷  (384 x E x I)  

L =    ³√ ((384 x σ x E x I) ÷ (5 x F))

I =      b x h³  ÷   12

Where:

σ  =  deflection

F  =  Force in Newtons

L  =  Span

E  =  Modulus of Elasticity in N/mm²

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:

σ =       (F x L ³)  ÷  (384 x E x I)

L =    ³√ ((384 x σ x E x I) ÷ F)

I =      (b x h³)  ÷  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.

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.

The average weight of standard books per 500 mm run:

Small paperback                                      8 ½  X  5  ½  inches       10.29 Kg  

Small modern compact paper backs        8 ½   X  6 inches            15.7 Kg

Small hardback older book                      9  X  6 inches                 11.84 Kg   

Medium hardback book                           10  X  7 ½ inches           17.4  Kg    

Large hardback book                                12  X  9 ½  inches          37.2 Kg     

revised and uploaded 6th February 2005