Try the Interactive Calculator
Calculate results, get Excel formulas, and see worked examples
Open CalculatorAll Structural Vertical Bredth PE Equations (9)
-
Active Earth Pressure Resultant
Resultant active earth force and location on a level-backfill retaining wall.
intermediateHigh Frequency -
Beam Deflection – Uniform Load, Simple Span
Maximum midspan deflection of a prismatic simply supported beam under uniform load.
intermediateHigh Frequency -
Elastic Flexural Stress in a Beam
Maximum bending stress from a given bending moment using elastic section properties.
basicHigh Frequency -
Simply Supported Beam – Uniform Load (Vmax & Mmax)
Maximum end reaction, shear, and midspan moment for a simply supported beam with a full-length uniform load.
basicHigh Frequency -
Concrete Beam Nominal Flexural Strength (Rectangular Section)
Nominal flexural strength of a singly reinforced rectangular concrete section using an equivalent rectangular stress block.
intermediateHigh Frequency -
Euler Buckling Load (Pinned–Pinned)
Critical buckling load for an ideal pinned–pinned column (extend with K for other end conditions).
intermediateHigh Frequency -
Footing Bearing Pressure
Average soil bearing pressure under a concentric rectangular footing.
basicHigh Frequency -
LRFD Gravity Load Combination (Example)
Example LRFD gravity load combination with dead, live, and snow/roof loads.
basicHigh Frequency -
Tributary Area Line Load
Converts a uniform floor/roof surface load into a line load on a beam or joist using tributary width.
basicHigh Frequency
Frequently Asked Questions
How do I use Active Earth Pressure Resultant on the PE exam?
On the PE exam, Ka is often given or must be calculated from Rankine theory: Ka = tan²(45° - φ/2). Remember the resultant acts at H/3 from the base for triangular pressure distribution. This force is used in overturning moment calculations as Pa × (H/3).
How do I use Beam Deflection – Uniform Load, Simple Span on the PE exam?
This is THE most common deflection formula on the SE exam. Memorize it! Always check units carefully - use consistent systems (kip-in-ksi-in⁴ or N-mm-MPa-mm⁴). The constant 5/384 = 0.01302 can speed calculations. Remember to compare to code limits: L/240 for live load, L/180 for total load in many codes.
How do I use Elastic Flexural Stress in a Beam on the PE exam?
This is THE most fundamental flexural equation on the SE exam. Watch units carefully - moment and section modulus must be consistent (kip-in with in³, or N-mm with mm³). Often combined with interaction equations for beam-columns. Steel code problems frequently give section properties directly.
How do I use Simply Supported Beam – Uniform Load (Vmax & Mmax) on the PE exam?
This is the most fundamental beam equation - memorize the coefficients 1/2 for shear and 1/8 for moment. Watch for problems that give total load instead of unit load (divide by L first). Maximum moment always occurs at midspan for uniform loads.
How do I use Concrete Beam Nominal Flexural Strength (Rectangular Section) on the PE exam?
This is a fundamental concrete flexure equation appearing on every SE exam. Always check units carefully - use consistent systems throughout. Remember that 'a' is the depth of the equivalent rectangular stress block, not the neutral axis depth. For T-beams or doubly reinforced sections, use different equations.