Introduction to Loads and Forces

1. Introduction

This was actually a part of a lesson that was just way too long.

Anyway, here we go ...

2. Live Loads

Loads on structures fall into two big categories: 1) weight loads of the building itself (material weights), and 2) live loads. Live loads in a broad sense include wind loads, snow loads, earth pressure loads (e.g., backfill against walls below grade), seismic (earth shaking) loads, and loads due to people occupancy and use, though live loads can also mean just the loads due to occupancy. More precisely, we will use loads as defined in the International Building Code (IBC), Chapter 16, as follows:

Ones that we will spend a lot of time looking at ...

D or DL ... Dead loads

L or LL ... Live loads, including loads due to occupancy, sometimes called Occupancy loads

L_r ... Roof Live load (used where there isn't much snow on roofs)

S or SL ... Snow loads

One that we will spend some time looking at ...

H ... lateral earth pressure loads

Ones that we won't spend much time looking at ...

W ... wind loads

E ... Earthquake loads

Others that we will not look at ... (so why am I even mentioning them???)

F ... Fluid loads, F_a ... Flood loads, P ... Ponding loads, T ... Self-straining forces loads

Oftentimes we will see `R' in front of loads ... denoting `Roof' ... such as RDL ...

Or `F', denoting `Floor' ... FLL for Floor Live load, FDL for Floor Dead load, and so on.

Minimum values for all of these loads are provided (`prescribed') in the model and/or local codes.

Some prescribed minimum loads that we will use much in this course are ...

From IBC TABLE 1607.1 Minimum ... Live Loads

Under Residential ...

All areas except balconies and decks ... 40 psf

Habitable attics and sleeping areas ... 30 psf

Under Office buildings ...

Lobbies and first floor corridors ... 100 psf

Offices ... 50 psf

Corridors above the first floor ... 80 psf

Balconies* ...

Exterior ... 100 psf

One and two-family residences not exceeding 100 sq.ft. ... 60 psf

Roofs ...

Roof loads depend on locale and the use of the roof. In areas with significant snowfall the design of the roof will be dependent on the Snow load, and any other `things' on the roof (mechanical equipment, etc.). Contact the local building authority for minimum roof load requirements or guidance. In cases where roof load requirements are not provided by the building authority the designer may need to determine the roof load based on surrounding snowfall information. It appears to the trend where I practice for building officials to provide `ground snow load' information, from with the designer must determine the roof loads. A `primer' type article on determining roof snow loads from ground snow loads is ... here.

* Obviously in areas with significant snowfall the exterior balconies may be required to carry more than these amounts, especially if the balconies are located in areas where they may potentially have to carry drifting and/or sliding snow and/or ice.

This is probably a good time to mention the `questionnaire'. I have put together a one-page sheet that I use for various projects on which I obtain and put the important information for my project. Some of this information I obtain from the Owner, some from the Building Official, and some from other. With this sheet in front of me I can hopefully ask the right questions early on, obtain the information I need, and be able to proceed with design in an efficient matter. Link to it ... here.

Note: you are going to see stuff in this questionnaire that you (now) recognize, and some that you don't. Some of this information you will simply pass on to your Structural Engineer, if need be.

3. Dead Loads

Dead loads are the `weights' of the building materials. These loads are generally calculated (specifically) since the building materials are generally known. You will find TABLE 4.1 Weight of Building Construction in the text quite helpful in this regard. With regard to any structural member or element, dead loads are:

1. Applied ... arising from what is being carried by the member, and
   
2. Self Weight ... the weight of the member itself.
   

The loads given in TABLE 4.1 are in `psf'. I call these `area loads'.

4. Area Loads

Symbol ... σ (sigma)

For example, ½ in. gypsum ceiling material is shown to weigh ... 2.5 psf (lb per sq. ft. of ceiling).

A wood rafter system made up of 2 x 10s @ 24 in. o.c. weighs ... 1.7 psf. Obviously this is an average, since there are 1 ft x 1 ft regions of roof with no 2 x 10s at all (in between the rafters).

If we want the weight of the whole roof system, we need to add up it's components.

For example ... a typical `light' roof system may consist of the following materials, with which I have included weights from the Table ...

Asphalt shingles and moisture barrier ... say 3 psf

½ in. wood sheathing @ 3.0 psf / in. is ... 1.5 psf

2 x 10s @ 24 in. o.c. ... 1.7 psf

Batt insulation ... 0.5 psf

½ in. gypsum ceiling ... 2.5 psf.

Total ... 9.2 psf

Let's use ... 10 psf

This is a pretty `lean' roof.

Note that this is for each sq. ft of the roof plane.

Many of our calculations are with based on `plan' area (the projection of the roof onto the ground below).

If the roof is sloped, then the `plan area' load is greater than the above value; an example follows of how to go from a roof plane to plan area value.

Determine roof angle (θ) as the tangent inverse of the rise over the run ...

... θ = tan ^-1 (V/H)

Then the weight in psf on the plan is the weight of the roof divided by the cosine of θ ...

If, for our example, we have a roof with rise/run = V/H = 6/12 ...

... θ = tan ^-1 (6/12) = 26.6 º ...

σ _plan = σ _{roof plane} / cos θ = 10 psf / cos 26.6 º

... 10 psf / 0.89 = 11.2 psf ...

Say, 12 psf

Obviously, for steeper roofs the difference between roof plane and projected area ... is even more.

With the above calculation as (kind of) an example, I often use the following estimated overall area loads for light frame roofs, walls, and floors.

Presumptive light frame construction system weights

Roofs ... 15 psf DL

Floors ... 10 - 12 psf DL

Int. walls ... 8 psf

Ext. walls ... 10 psf

NOTE: obviously if we use heavier (or more) materials, these weights go up.

5. Line Loads

Symbol ... ω ...

Let us now consider a beam supporting a portion the roof. How much the beam carries of the roof depends on how the roof contributes load to the beam. Often we think in terms of `tributary width' or `tributary area'. If the beam is a ridge beam, for example, going down the `middle' of the roof, and the roof is 40 ft wide, wall-to-wall, with the beam half way in between, the tributary width for the beam is ½ of 20 ft on each side, or a total (tributary width) of ... 20 ft.

The `line load' on the beam resulting from the weight of the roof (DL) is ...

ω _DL = σ _DL x trib width ...

Continuing with our example ...

ω _DL = 12 psf x 20 ft = 240 plf ... DL applied to the roof beam ...

Now let us say that the roof SNOW load is 40 psf ...

ω _SL = σ _SL x trib width = 40 psf x 20 ft = 800 plf ... SL applied to the roof beam

Note that we have NOT yet considered the (self) weight of the beam.

6. Self Weight

Here it is in equation-form ...

ω _{DL, sw} = γ x A ...

where γ is the specific weight of the material (lb per cu.ft.)

and

A is the cross section area of, in this case, the beam.

Using, for example, γ = 35 pcf for wood ... (heavy Douglas fir/larch) ...

And let's say the beam is 5-1/8 in. x 12 in. ...

ω _{DL, sw} = 35 lb/ft³ x (5-1/8 / 12 ft) (12/12 ft) = 15 plf

So, the beam carries ...

ω _TL = ω _SL + ω _DL + ω _{DL, sw} = 240 plf + 800 plf + 15 plf = 1055 plf ...

Note: if we want to include the weight of the beam in the `area load' of the roof ... we could take the 15 plf and divide by the tributary width ... to get ...

15 plf / 20 ft = 0.75 psf ...

So, overall, the beam would add about 1 psf to the `whole' weight of the roof.

7. References

International Building Code, International Code Council, 4051 West Flossmoor Road, Country Club Hills, IL 60478.

Simplified Engineering for Architects and Builders, Ambrose, J. and P. Tripeny, 10^th edition, John Wiley & Sons, Hoboken, New Jersey.