Joist and Beam Calculator

A Joist and Beam Calculator is used in construction to determine the correct size and spacing for beams and joists in a structure. Joists are horizontal supports that hold up floors, ceilings, or roofs, while beams carry the weight of the joists and distribute them to other parts of the building. This calculator ensures the size of beams and joists for safe support in the load by avoiding sagging or even complete structural failure.

By inputting details such as the type of material (like wood or steel), span length, load requirements, and spacing, the calculator provides precise recommendations. This helps builders and homeowners avoid costly mistakes and ensures the structure is safe.

These are joist and beam calculators that are used in building houses, decks, and commercial lots. They help save time, lessen waste of materials, increase compliance with building codes, and obtain a much safer and more effective construction process. This load, span, type of material, and local building codes are computed for the best-fitted specifications in its calculations.

Joists and Beam Calculation Procedure

An accurate count and size of joists and beams in a structural system are necessary. The size of the beams and joists is decided after carefully analyzing the material’s properties, conditions, and deflection criteria. For precise calculations for accurate quantities of materials and thus costs of materials in tune with project requirements and budgets, utilizing material takeoff can give you an exact amount and cost of materials needed for project management and budget adherence.

The following sections explain the core calculation principles and steps for determining the correct dimensions for your beam and joist.

Calculating of Joists

The dead load, the weight of the structure itself (such as floors, roofing, and walls), and the live load, which is the weight of moveable objects, including people, furniture, appliances, etc., are factors that determine the total load a joist will carry. For example, a typical residential floor might have varying dead and live load values according to local building codes.

Load per Unit Length Formula

• Total Load=Dead Load+Live Load

• Span Length: Distance between the support where the joists rest
• Load: The weight that each joist must support includes both live and dead loads.
• Material: This material is for joists because it affects load capacity.
• Joist Spacing: For most residential construction, the distance between joists is typically 16 inches in the center.

Example

• For a residential floor:
• Dead Load: 10 lb/ft2  (this might include the weight of the flooring, ceiling, and roof material).
• Live Load: 40 lb/ft2  (the weight of furniture, people, and appliances).

Add them up to get the total load per square foot:

• Total Load:= 10 lb / ft2+40 lb / ft2=50 lb /ft2
• This tells us that each joist needs to bear 50 lb/ft².

Determine the Total Load per Square Foot

The total load per square foot is the sum of the live and dead loads.

• Total load:= 40 per square foot + 10 per square foot = 50 per square foot

Formula: To find the load per linear foot.

• Load per linear foot: = total load × joist spacing
• 50psf x 1.33 feet: = 66.5 pounds per line foot, meaning that each joist will carry 66.5 pounds per linear foot.

Example: Let’s say that you are designing a floor system for a house under the following conditions:

• Span: 14 feet the distance between the support for the joists.
• Load: 50 pounds per square pound of food for the dead load (building materials) and 40 pounds per square foot for the live load (people, furniture, etc.)
• Material: Softwood (for example, pine) with a strength of 1,400,000 psi
• Joists spacing 16 inches on the center

Determine Joist Spacing

• The spacing between joists determines how much load each joist will carry. For most residential construction, joists are spaced either 16 inches or 24 inches apart, depending on the load conditions and material strength.

Example:

• If the joists are spaced at 16 inches:
• Spacing in Feet:=16 / 12=1.33 ft

Now, calculate the load carried per linear foot of the joist by multiplying the total load by the spacing in feet:

Load per Linear Foot=Total Load×Spacing in Feet

• Load per Linear Foot: = 50lb /ft2 x 1.33ft =66.5lb/ft. This means each joist carries 66.5 pounds per foot.

Calculate the Bending Moment

• The bending moment indicates the force that tries to bend the joist under an applied load. It is highly essential for the determination of the joist size. For a simply supported beam or joist that carries a uniformly distributed load, the bending moment is given as M= w x L2 /8

Where

M is the Bending Moment in units of foot-pounds or inch-pounds w Load per unit length in units of lb /ft L Joist span is measured in terms of feet.

Example

• Assume the joist span is 12 feet. From the load per linear foot of 66.5 lb/ft
• M = 66.5 x 1228 = 66.5 x 1448 = 1,429 foot-pounds

This is the moment that the joist must resist.

Calculate Joist Size

Its size is determined by the section modulus S, which depends on joist geometry. For a rectangle section, the following formula is used to determine section modulus:

• S= b×h2 / 6

Where,

• b = Width of the joist in inches.
• h = Height of the joist in inches.

Example

• Take it that the material of the joist has a section modulus of 40 in3, and the bending moment is 1,429 foot-pounds or 1,429 × 12 = 17,148 inch-pounds.

Calculate the required section modulus

• Section Modulus=17,148 / 40 = 428.7 in3

This means that the joist must have at least a section modulus of 428.7 in³ to safely bear the load.

Verify Deflection Limits

The deflection is the amount by which the joist will bend under the load. It is usually calculated to ensure that the bending is within acceptable limits. Building codes typically require that the deflection be no more than L/360, where L is the span of the joist.

The formula for deflection is

5wL4 / 384EI

Where: 

Maximum deflection (in inches).

• w = Load per unit length (in lb/ft).
• L = Length of the joist (in inches).
• E Elastic modulus of the material (in psi).
• I = Moment of inertia (in4).

Let’s take

• Load per unit length:= 66.5 lb/ft, which has been converted to 5.54 lb/in.
• Span:=12 feet, thus 144 inches.
• Modulus of elasticity(E):=1,600,000 psi
• Moment of inertia(I):=40 in⁴
• Now compute for the deflection.
•  5× 5.54× 144(4)/384× 1,600,000×40

This will give a deflection result that can be compared to the L/360 limit to determine whether the joist is appropriate for the application.

Calculation for Beams

It gets complicated since loads to beams come from several joists and get redistributed to the wall or columns. The beam is supposed to have a sufficient cross-section to accommodate the loads coming in from the many joists it supports. Understanding the proper beam sizing requires computation with regard to beam strength, the length of span involved, and the overall load carried.

Calculating Total Beam Load

Before we do anything, let us first collect information about the beam. The information you will gather is as follows:

• Load or w: These are the overall weights that a beam carries to its load that may be both permanent and temporary. A very good example could be the floor weight plus the furniture or people on it.
• Span or L: This is simply the length of a beam between the two supports.
• Material: Different materials can have different strengths or may be steel, wood, or concrete

Beam Support Type: The load will be placed differently on a simply supported or fixed beam when compared to a cantilever beam.

Example: Consider a simple beam with the following properties.

Load (w) = 150 lbs/ft (this means the beam carries 150 pounds of weight for every foot of its length)

Span (L) = 12 feet

Material = Wood (with an allowable stress of 1,000 psi)

Calculate the Bending Moment

This bending moment is what causes the beam to bend. Now, using a simply supported beam with a uniform load, the bending moment at the center can be calculated using the following formula:

M = w x L2 / 8

Where

• M is the bending moment in foot-pounds or inch-pounds,
• w is the load per unit length in lbs/ft,
• L is the span of the beam in feet.

Example

Now, putting in our values:

Load (w) = 150 lbs/ft

Span (L) = 12 feet

Now, let’s calculate the bending moment

M=150 ×1228 =150 ×1448 = 2,700 foot-pounds

This means that at the center, the beam will have a bending moment of 2,700 foot-pounds.

Calculate the Section Modulus

The section modulus is a measure of how much resistance a beam has against bending. It is determined by dividing the bending moment by the allowable stress of the material.

The formula is

S= M / allowable stress

Where:

• S is the section modulus (in inches2),
• M is the bending moment (in inch-pounds),
• Allowable stress of the material (in psi).

Example

Let’s assume that the allowable stress for wood is 1,000 psi. We have to first convert the bending moment from foot-pounds to inch-pounds since the section modulus is measured in inches:

• M=2,700 foot-pounds x 12=32,400 inch-pounds

Then, let’s calculate the section modulus:

• S=32,4001,000=32.4 in3

That translates to a section modulus of the beam of more than 32.4 cubic inches to prevent its bending due to force.

Evaluate Beam Deflection

Deflection refers to the extent to which the beam is expected to bend. Too much bending might lead to structural problems, hence checking that this should not occur.

The equation for deflection is as shown:

• D = 5×w× L4 384× E× I

Where

• D = Deflection in inches
• w = load per unit length (in lbs/ft)
• L = span (in feet)
• E = modulus of elasticity of the material (in psi)
• I = moment of inertia (in inches⁴), which is a function of the shape of the beam.

Example:

Suppose we know that the modulus of elasticity (E) for the wood is 1.6 million psi, and the moment of inertia (I) is 20 inches4. Now, we will compute the deflection.

• D =5×150×124384×1,600,000×20

To obtain the final answer, we simplify and get the following: D=0.0043 inches.

This is an extremely small deflection. Thus, the beam would be able to support the load with very minimal bending.

Final Beam Sizing

Finally, we select the correct size of the beam. Using the section modulus from step 3 and deflection from step 4, we choose a beam that satisfies those demands.

Example

Section modulus required = 32.4 in3. The table of sizes for the beams would be used to pick up a beam that has a minimum section modulus of 32.4 in3.

You will want to check, too, that the deflection calculated in step 4 is acceptable. You know that for simple beams under load, this may not exceed L/360 or for commercial buildings, L/240.