Challenge 001 — Learn units

Four short units, one for each part of the job. Read them before your brief, or come back when a step sends you here. Each unit ends with three questions, and the answers are at the bottom of the page.

These numbers are not yours. Every example and every question on this page uses a practice bracket that no student is ever given. The method is the one your challenge checks. The numbers never are.

The practice bracket

The same kind of part as yours: one flat steel plate standing on edge, bolted to a column at one end, with a mass hanging near the other. Different numbers, and a different steel on purpose. Yours is in your brief.

Unit 1 · The load

A mass is not a force. The brief gives you a mass in kilograms. What the bracket feels is its weight, a force in newtons:

W = m · g

A mass written where a force is asked for is wrong by a factor of about ten, and the units say so before any grader does: kg is not N.

A force at a distance is a moment. The bracket is a cantilever, held at the bolts and free at the other end. The load bends it hardest at the root, where it is held, and the moment there is the force times its lever arm:

M = W · L

Two things to get right:

• The lever arm is L, measured from the centre of the bolt pattern. Not from the column face, and not from the end of the plate.
• The whole load hangs at one point, at the end. A formula with L/2, L/4 or L² in it belongs to a different beam: a load at mid-span, a beam on two supports, or a load spread along the length. This bracket is none of those.

Worked, on the practice bracket:

Keep newtons and millimetres all the way through. A moment in N·mm divided by an area in mm² is a stress in MPa, which is where Unit 2 begins.

Check yourself

1. A shop sign of 35 kg hangs from a bracket. What force does it apply, in N?
2. The sign hangs 350 mm from the centre of the bolt pattern. What is the bending moment at the root, in N·mm?
3. On another bracket the load hole is 390 mm from the column face, and the centre of the bolt pattern is 40 mm from the column face. Which lever arm do you use? (a) 390 mm (b) 350 mm (c) 40 mm

Unit 2 · The section

The safety factor goes on the material.

σ_allow = Re / n

The yield strength divided by the safety factor: never multiplied by it, and never left out. Putting the factor on the load instead reaches the same thickness by another road. The brief asks for this road so that every step can be checked (brief §6).

The section modulus says how much bending a shape can carry. Bending stress is the moment divided by the section modulus, σ = M / Z. Set the stress to the allowable one and turn it round:

Z_req = M / σ_allow

Moment over stress: not times, and not the other way up. The units check it for you, because N·mm divided by MPa is mm³, and mm³ is what a section modulus is measured in.

The plate stands on edge. The load is vertical and the plate is vertical, so the plate bends in its own plane and its depth b is the depth of the beam. For a rectangle:

Z = t · b² / 6

The depth is squared and the thickness is not. That is why a plate on edge is stiff and the same plate laid flat is floppy. Swapping them, b · t² / 6, is the most common mistake on this challenge. And do not confuse Z with the second moment of area I, which is Unit 3's quantity.

Solve for the thickness, then buy one that exists.

t_req = 6 · Z_req / b²

Nobody sells plate of exactly the thickness your calculation gives. Take the smallest stock thickness that is at least t_req. Always go up, never to the nearest: rounding down leaves a plate weaker than your own calculation says it must be.

Worked, on the practice bracket:

Check yourself

1. A bracket in S355 steel (Re = 355 MPa) is designed with a safety factor of 2.5. What is the allowable stress, in MPa?
2. A plate 8 mm thick and 30 mm deep stands on edge under a vertical load. What is its section modulus, in mm³?
3. Your calculation needs a plate at least 8.2 mm thick. From the stock list above, which thickness do you buy, in mm?

Unit 3 · Stiffness

Strong enough is not stiff enough. A plate can carry its load without yielding and still sag where everyone can see it. So the brief sets a second limit: the free end may move down by no more than L / 300.

For a cantilever with a point load at its free end, the tip deflection is:

δ = W · L³ / (3 · E · I), with I = t · b³ / 12

• I is the second moment of area. The depth is cubed this time, and the depth is still b.
• The 3 belongs to this beam. Other beams have other numbers in that place: a beam on two supports loaded at mid-span, or a load spread along a cantilever. Neither is this bracket.
• Use the thickness you would buy, not t_req. The deflection that matters is the one of the plate you would actually bolt up.

Then decide. If the deflection is within the limit, strength governs and the thickness you bought stands. If it is not, go up the stock list one size at a time until it is. The thickness you use is the smallest stock size that passes both checks.

Worked, on the practice bracket. The limit is 440 / 300 = 1.4667 mm.

On the practice bracket deflection governs. Strength alone said 8 mm; the plate you use is 12 mm. Stop at step 6 and you would ship a bracket that bends too far. On other numbers strength governs instead, and the only way to know which is to check both.

Check yourself

1. The shop sign from Unit 1 hangs 350 mm from the bolt-pattern centre, on a steel plate 8 mm thick and 30 mm deep (E = 210 000 MPa). What is the tip deflection, in mm?
2. Keep everything the same, but make the plate twice as thick. The tip deflection becomes: (a) half as large (b) an eighth as large (c) a quarter as large
3. A bracket carries 400 N at 380 mm, on a plate 35 mm deep. Strength needs at least 5.4 mm, and the deflection limit is L / 300. Which stock thickness do you use, in mm?

Unit 4 · The model

The numbers are done. What the checker measures now is your part.

• These must be exactly your numbers: the plate depth b, the projection L, the four bolt holes on their p_h × p_v rectangle, the load hole, and the thickness you gave at step 8. Five holes in all.
• Distances between features, never positions in space. It does not matter where your origin is, which way up the plate lies, or which axis you called vertical. Model it however is comfortable.
• L starts at the centre of the bolt pattern. A reliable way to get it right: sketch the four bolt holes symmetric about a centre point, then dimension the load hole from that point, not from an edge. The number you type is then L itself.
• The free end is yours. Square, radiused or chamfered, with or without fillets. None of it is checked against a number.
• One part, one solid, in millimetres. No bolts, no column, no shackle. Check the document's units before you export.
• Export STEP, AP203 or AP214. Not your CAD program's own file format, which only that program can open, and not an STL mesh, which has lost the exact holes the checker measures.

Check yourself

1. Which file do you send? (a) the part file your CAD program saves (b) an STL mesh (c) a STEP file, AP203 or AP214
2. You modelled the plate lying flat, with the origin at one of the bolt holes. What happens? (a) it fails: the origin must be at the bolt-pattern centre (b) it fails: the plate must stand on edge in the model (c) nothing: only distances between features are measured
3. Which of these must equal your own numbers? (a) the radius at the free end (b) the plate depth b (c) the size of the edge fillets

Answers

If one of yours differs, go back to that unit's worked example and follow your numbers through it line by line. The step where your working and the example's part company is the step to look at.