How can I predict how much weight my bridge will hold?

Short answer: you can estimate it, and find the weak member, but you can't predict it exactly. Balsa varies from stick to stick and glue joints vary from builder to builder, so test as well as calculate.

A practical approach

1. Find the force in each member for a given load. See calculating forces.
2. Estimate what each member can carry. Short sticks can take a push up to about their crushing strength, while long ones buckle at a much lower load. See preventing buckling and how strong balsa is.
3. Check each joint. Joints often fail first. See why bridges fail.
4. The weakest part sets the limit. The load that makes the first member reach its limit is your estimate.
5. Test a practice bridge and compare it with the prediction. The gap tells you what you missed.

Why predictions are rough

• Balsa strength varies by 15 to 25% even at the same density.
• We haven't yet had controlled tests of hobby glue joints on balsa, so joint strengths are estimates.
• Real joints carry some bending, which a simple model ignores.

Treat a prediction as a way to compare designs, and test to find out. See testing safely.