VERTICAL SHEAR IN BEAMS

Vertical shear stress distribution in beams:

Remember that shear acts normal (perpendicular) to the beam. A simply supported beam with a concentrated load in the center of so many (say 10) pounds carries the load equally to the two supports, each taking half. Therefore, the vertical shear “up” (+) at the left support is one-half 10=5, and this shear is the same along the beam until the center. At the center, the “up” shear is decreased by the load 10 to equal 5 “down” (-) on the remaining portion of the beam over to the right support. Therefore, a beam carrying a concentrated load has large total shear at the load point.

Now let’s change the concentrated load into a uniform load spread along the beam. What happens to the shear stress in the beam? The load on the supports is the same, (the reaction), but now the shear stress decreases uniformly to zero at center span, where its “sign” changes and then its magnitude increases to the support.

Therefore the shear in a uniformly loaded simple span beam is zero at mid-span, but maximum at the supports. This is more significant information for deciding where (or if) to poke holes in the beam.

(Beams are also subject to horizontal shear developed by the opposing tension and compression forces. The shear plane is located at the neutral axis. Review of this stress must be made by a design professional.)

Summary of important stuff for placing and modifying beams:

For the most part, the beams we erect are considered to be uniformly loaded and simple span, in which the middle third of the span is the most critical area for moment stress, and the outer thirds are the most critical for vertical shear stress.

Beams should not be cut on the tension side in the center third.

The web should not be cut near the supports or load points of beams carrying heavy shear.

The web may be cut through at the neutral axis at mid-span.

Sawn lumber having loose knots, check, splits, or damage should be placed so these defects do not compromise strength.

Continuous beams have moment reversal over the interior supports. That is, the top flange is in tension there. Tension also appears in the top flange at the support in cantilevered beams. Rules for making cuts or holes in beams should be recognized in these situations.

Plywood, when loaded in beam action (as in roof sheathing or flooring) must be laid so that the face grain is perpendicular (normal) to the supporting beams. This placement provides the stiffest resistance to bending. Plywood is very weak in bending across the face grain. It is a bad mistake to lay up plywood improperly.

COLUMNS AND TIES

Columns AND TIES (Compression and tension resistance)

A Column is a member resisting axial compression forces. Column connections are usually in direct end bearing. Studs are columns, as are posts and struts. Length and condition of lateral (sideways) support classify columns as either “long” or “short”. Struts are short columns, resisting loads by pure compression strength.

Long columns are subject to buckling, in which the loaded column can be deflected out of line and fail by a combination of compression and bending. Loads on long columns are governed by what is called the L/d or “slenderness” ratio, i.e. the length of column that is laterally unsupported (L) divided by the least dimension (d) of the column. This ratio should be less than 50. Long column load capacity varies inversely as the square of this ratio, i.e. capacity decreases as the ratio increases. See the Column table for more data.

A tie is the reverse of a column, in that it resists axial tension forces. Temporary bracing is often in tension. Permanent tension members are common in trusses, uncommon elsewhere. Tie connections place shear on connecting hardware.

ROOF TRUSSES

ROOF TRUSSES

Even though it takes loads similarly to a beam, a truss is not a beam but a space frame with several connected members acting in either tension or compression. It is designed to carry heavy loads across long spans. Trusses can be thought of as open-webbed beams, in that the top flanges (chords) are in compression, and the bottom chords are in tension. These chords may also carry moment, depending on how load is transferred to the truss. The individual web pieces are either in tension or compression, depending on how the truss is configured. Connections at truss joints are critical; they should not be compromised through additional carpentry.

Since they are strong in one direction but weak in another, trusses, especially light trusses, must be handled with care. During erection, they can easily tip if not securely braced. When framed for loading, the top chords must be carefully aligned and straightened, uniformly spaced and parallel, and with the truss webs vertical or nearly so. Since the bottom chords will be in tension when fully loaded, less care needs to be given to aligning them. Obviously, the chords must not be damaged.

When placing roofing on trusses, try to keep the roofing operations more or less equal on each side, i.e. do not complete one side then do the other. Asymmetrical loading will introduce un-balanced horizontal thrust in the truss. This is more critical on steeper pitches.

NAILED JOINTS

NAILED JOINTS

Joints connecting structural members are essential to the strength and performance of the building. They are usually the “weakest link”. Until framing anchors came along, nails were about the only way to hook two pieces of wood together cheaply and quickly. Framing anchors usually transfer loads through nails or screws in shear.

Side, toe, and end nailing are still common methods of connection. Nailing is actually a poor way to connect lumber, since it takes many nails to transfer the inherent strength of wood. Moreover, quality control is difficult, and there are many variables than cannot be evaluated. Never-the-less, we still nail because it is fast, economical, and most everyone can swing a hammer.

Nails should be placed in a triangular or staggered pattern. Avoid placing more that one nail into an individual growth ring. Beware of over-nailing. The last nail you place may end up splitting the piece, compromising the joint. Then what will you do?

When connecting temporary braces use a double headed nail; but if using a regular nails, try not to nail flush, instead leave about 1/8 inch proud for ease in withdrawal when dismantling. This has safety implications.

Edge nailing: When connecting members loaded in transverse shear (i.e. beams), be careful to avoid placing nails too close to the edge on the loaded side. Confine your nails to the “lower” 2/3 of the piece.

Toe nail or not toe nail? That is the question. You learned in high-school wood shop that toe nailing is a good thing. Maybe, maybe not. Remember that forces operate in a straight line. A nailed joint transfers loads by shear or withdrawal (tension). Nails driven straight (normal) into a joint provide better withdrawal resistance against normal loads than nails on a slant. Can you draw the force resolution to demonstrate this?

The power nailer is a mixed blessing. It is handy for placing nails without hammering, when hammering will disturb the joint arrangement. It is also faster than hand nailing. But it is dangerous to use, especially in the hands of the novice. Its ease and speed makes it the frequent cause of over-nailing, which can actually weaken joints. For temporary framing of braces, etc. it is a bane, since too many nails often are placed and usually placed too deeply for ease in dismantling.

THREE B's

THREE B’s

(No, not those three Lutheran guys Beethoven, Brahms, and Bach. They weren’t famous for their carpentry.)

Blocking is installed in stud walls for several reasons. Blocks are placed to prevent “chimneys” for fire protection, and to provide a nailing surface for sheet rock, etc. Blocks add to wall strength by reducing the “L/d” ratio.

For sheet rock and other cladding, accurately spaced, parallel studs are necessary. Studs can easily be shoved out of parallel by careless blocking, with either too long or too short blocks. Because studs themselves may be warped, the block will often not fit snuggly. Measure the actual space between the stud pairs at the nearest plate to the block, and subtract 1/16 inch for the cut length. This will help maintain the studs parallel or nearly so after the whole wall section is blocked.

When possible, stagger the blocks around the line, with a 1/3 to ½ overlap. This permits direct end-nailing of blocks, in lieu of toe nailing.



Bridging enables neighbor beams to “share the load” under a floor or roof, and provides lateral stability. Bridging used to be made from two pieces and placed in an X pattern; this has given way to using solid sawn wood. As in blocking, achieving parallelism in the beams is important.

Bracing can be temporary or permanent. Remember that forces act in a straight line. Determine the direction of the force you are bracing against, and place the brace in direct linear opposition to it. Brace from “flimsy” to “stout”, not from “flimsy to flimsy”! Efficient bracing makes triangles, (sometimes imaginary) with two points of the triangle at the ends of the brace, and the third point at the intersection of a line along a solid base in the plane of the triangle.

Visualize how the force in a brace will resolve into horizontal and vertical components at the end points. A steeply sloping wall brace will have a smaller horizontal component than a flatter brace, but larger vertical component, and vice versa. A steep brace will have less resistance to the wall over-turning, but a flatter brace will be longer and heavier (assuming it’s attached to the wall at the same point). The best slope of the brace is about 45 degrees. Paradoxically, compression braces to a free-standing wall will actually introduce overturning forces into the wall, the same forces the brace is to resist, so be careful not to apply excessive lateral bending forces with the brace. Braces in compression are less effective than braces in tension. Because a brace in compression acts as a column, its strength and stability is diminished unless it is stiffened along its side. Since temporary braces will be removed, avoid over nailing and remember to leave the nail head proud about 1/8 inch for ease in withdrawing.

Double cross (X) braces not connected at the crossing point will be unstable, unless the brace makes a complete triangle with all three end points fixed.

A final word on the Bs: Do not block the bottom chords of light trusses until they are fully loaded, or nearly so. Remember these chords are in tension and will straighten on their own. Premature blocking may inhibit this, and in extreme cases introduce unwanted tension or lateral stress in the chord.

Also, temporarily brace the top chords of TJIs, etc. against overturn, but it is foolish to waste time bracing their bottom chords.

SUMMARY OF FRAMING RED FLAGS

SUMMARY OF FRAMING RED FLAGS

Beams: Protect the bottom flanges from cutting and other damage, and place sawn beams to take account of flaws (loose knots, splits, etc).

Trusses: Beware of pre-mature blocking of bottom chords. Be careful against damaging joints and cutting individual members. Be careful to avoid asymmetrical loading when installing roofing. Avoid using truss tension members as beams; if necessary to place heavy loads on the bottom of a truss, place the load point at or near a truss joint.

Plywood: For roofs and floors, be sure the face grain is normal to the support frame.

Re-roofing: Beware of roofing over an existing roof. Check dead loads.

Joints: Be careful not to over-nail.

Temporary Columns: Watch out for excessive un-supported length.

Double cross-braces: Be sure they are also connected together at the crossing point.

Manufactured members: Follow manufacturers’ recommendations for handling and temporary bracing.

GEOMETRY: MISFITS AND DISTORTIONS

GEOMETRY

MISFITS AND DISTORTIONS

“All lumber should be cut to exact dimension and straight without warp, twist, wane, or split. Walls and columns should be exactly vertical. Floors should be perfectly flat and level. Foundations should be at the precise elevation, absolutely straight and level. Stairs and roofs should have exact slope or pitch. Joists and studs should be uniformly spaced and perfectly parallel. Door frames and corners should be square to within an arc-second. Trusses should be straight as a fiddle string. Square and bevel cuts should be right-on and straight clear through. All joints should fit snuggly without gaps or warping. All connections should join evenly for a smooth surface”.

Sadly, the above ideals cannot be achieved in this sinful world even individually, let alone all together! A skilled carpenter knows how to remedy flaws and recover from errors, without resorting to “Cut to fit, warp to connect, grind to bear, and paint to match” – hopefully this common solution will be used sparingly. A wise worker also pays attention to manufacturers recommendations when installing fixtures, etc. The common solution of “using a bigger hammer” to make things fit should be avoided!

Distortions from the desired geometry can be due to many factors. Sections built off-site have to be transported, which can stress and alter their shape. Tall, narrow sections are difficult to build true to square and parallelism. Wood changes dimension across grain, (but is stable along grain) and it warps and twists. Concrete cannot be placed absolutely flat. Plumb and level is hard to verify over long distance with only a spirit level.

Spirit levels, tapes, and string lines are the usual tools we use to layout, control, and check the geometry and construction. Optical and laser instruments are now found on many projects, and can provide greater accuracy. Unfortunately, these tools are often misused, their relative accuracy or reliability not understood, and the relative importance of geometrical elements is frequently not recognized. When things don’t fit right, what should give: line, grade, level, plumb, straight, flat, smooth, parallel, square, spacing, pitch, or dimension?

The best answer to this question will vary depending on several factors. Some things are critical, others of minor importance. There is distinction between what should be nearly perfect vs. what can be barely adequate. Is the defect potentially dangerous, just ugly, or merely annoying? What crooked piece is the likely cause of the trouble? What reference line or measurement mark is most susceptible of error or mistake in determination and therefore most suspicious?

Some parts that are especially critical are door posts, wall corners, and joists and studs to which sheathing is attached. Interior “non-edge” misaligned studs can be tolerated, providing they are securely blocked. Some things that are out of level, plumb, or square, may be tolerable if they are to be covered, are not critical structurally, and providing the defect is not too egregious.

It’s probably safe to say that most misfits occur because of defective measuring, sloppy marking and cutting, and careless fastening, abetted by warped lumber.