Question 1

What is the maximum bending moment for a simply-supported beam with a UDL?

Accepted Answer

For a simply-supported beam of span L (m) carrying a uniformly distributed load w (N/m): Maximum bending moment: M_max = wL²/8, occurs at midspan. Maximum shear force: V_max = wL/2, occurs at the supports. Maximum deflection: δ_max = 5wL⁴/(384EI), occurs at midspan. Reactions: RA = RB = wL/2 (symmetrical). Example: A 6m simply-supported IPE300 beam supporting a 15 kN/m UDL (dead + live load): M_max = 15 × 6² / 8 = 67.5 kN·m. V_max = 15 × 6 / 2 = 45 kN. These are unfactored values — apply load factors as per SANS 10160 (1.2DL + 1.6LL) for structural design. In South Africa, SANS 10162-1 governs steel structural design (based on CSA S16).

Question 2

How do I calculate beam deflection and check it against allowable limits?

Accepted Answer

Deflection formulas for common beam configurations: Simply-supported + UDL: δ_max = 5wL⁴/(384EI) at midspan. Simply-supported + central point load: δ_max = PL³/(48EI) at midspan. Cantilever + UDL: δ_max = wL⁴/(8EI) at free end. Cantilever + tip point load: δ_max = PL³/(3EI) at free end. Where E = elastic modulus (Pa), I = second moment of area (m⁴). Allowable deflection limits per SANS 10160 / SANS 10162-1: Floors (general): L/360 live load or L/250 total load. Roof purlins: L/200. Beams supporting brittle finishes (tiles, plaster): L/360. Crane beams: L/600. Example: L = 6m, IPE300 (I = 8356 cm⁴), E = 210 GPa, w = 15 kN/m: δ = 5 × 15000 × 6⁴ / (384 × 210×10⁹ × 8356×10⁻⁸) = 18.9 mm. Allowable (L/360) = 6000/360 = 16.7 mm → IPE300 slightly overstressed — select IPE360.

Question 3

What load factors should I apply to beam loads in South Africa?

Accepted Answer

SANS 10160-1 (Basis of structural design) defines the following load combinations for ultimate limit state (ULS): Fundamental: 1.2DL + 1.6LL (dominant). Serviceability (SLS): 1.0DL + 1.0LL for deflection checks. Wind dominant: 1.2DL + 1.3WL + 1.0LL. Key load types: Dead load (DL / Gk): Self-weight of structure and permanent fixtures. Live load (LL / Qk): Imposed loads per SANS 10160-3 — offices 2.5 kPa, storage 7.5 kPa, plant rooms 7.5 kPa. Wind load (WL / Wk): Per SANS 10160-3. This calculator performs elastic analysis at the applied load — users must ensure the input load is the appropriate factored or unfactored load for their design basis.

Question 4

How do I select the right steel section for a beam?

Accepted Answer

Step-by-step beam selection: 1. Determine unfactored loads (DL, LL). 2. Apply ULS factors per SANS 10160: M_design = 1.2DL × L²/8 + 1.6LL × L²/8. 3. Select a section where M_cap = fy × Z ≥ M_design (elastic moment capacity), where fy = yield strength (MPa), Z = elastic section modulus (cm³). 4. Check deflection at SLS (unfactored loads): δ_max ≤ L/360. 5. Check shear: V_max ≤ 0.66 × fy × Aw (SANS 10162-1), where Aw = web area. 6. Check local buckling, lateral-torsional buckling if beam is long and unrestrained. Practical rule: For typical office floor beams at 1.5–3m spans, IPE180–IPE240 is common. For 6–9m spans with 10 kN/m UDL, IPE330–IPE450 is typical. SANS 50025 table gives South African available sections — specify these when ordering from local steel service centres.

Question 5

What is the difference between a cantilever and simply-supported beam formula?

Accepted Answer

Simply-supported beam (restrained at both ends against rotation-free vertical movement): Both ends allow rotation but not vertical displacement. The beam deflects downward with maximum deflection at mid-span for symmetrical loading. Maximum moment is at midspan for UDL or at load position for point loads. Cantilever beam (fixed at one end, free at other): Fixed end provides full moment restraint and reaction. Free end is unsupported and deflects maximally. Maximum moment occurs at the fixed end. Cantilever beams are inherently less efficient — for the same loading, a cantilever has 4× the maximum moment and 8× the deflection of a simply-supported beam of the same span. For retrofitted cantilevers in South Africa (e.g., access platforms, loading ramps), the fixed-end connection must transfer the full cantilever moment — connection design is critical and should be verified by a structural engineer.

Question 6

What is the second moment of area (I-value) and why does it matter?

Accepted Answer

The second moment of area (I, also called moment of inertia) quantifies how a cross-section resists bending. Higher I = stiffer beam = less deflection. I is calculated as: I = ∫y² dA over the cross-section. For a solid rectangle: I = bd³/12 (b = width, d = depth). For steel I-sections (IPE, HEB), the flanges are positioned far from the neutral axis to maximise I for a given weight. Doubling the I-value halves deflection. Doubling the depth d increases I by 8× (since I ∝ d³ for a rectangle). This is why deep, slender beams are preferred for spanning large distances. Second moment of area is also critical for Euler column buckling: P_cr = π²EI/(KL)², so slender columns with large I are less susceptible to buckling.

Question 7

How do I analyse a beam with multiple loads?

Accepted Answer

For beams with combined UDL and point loads, use superposition: 1. Calculate reactions, moments, shear, and deflections separately for each load case. 2. Add all contributions algebraically. Example — simply-supported beam under both UDL (w) and central point load (P): M_max = wL²/8 + PL/4. V_max = wL/2 + P/2. δ_max = 5wL⁴/(384EI) + PL³/(48EI). Superposition is only valid for linear elastic structures (no plastic hinges, no large deflections). In South Africa, structural analysis software commonly used: PROKON (South African origin, widely used), STAAD.Pro, SAP2000, Robot Structural Analysis. For complex beams, frames, or slabs, software is mandatory. Simple beam checks for platforms, lintels, and walkways can use this calculator as a preliminary sizing tool.

Question 8

What steel sections are available from South African steel suppliers?

Accepted Answer

South African IPE and HE sections are imported from Europe (ArcelorMittal, Tata, SSAB) and locally rolled by AMSA (now defunct) or imported. Commonly stocked in South Africa: IPE sections: IPE100 to IPE500 — widely available from BSi Steel, Macsteel, NJR Steel, Triomf Steel. HEA/HEB sections: HEA140 to HEA400, HEB140 to HEB400 — available on order. Channel (UPN/PFC), Angle (L), Hollow Sections (RHS/SHS/CHS): widely available off the shelf from BSi Steel and Macsteel. South African standard: SANS 50025 (identical to EN 10025-2) covers hot-rolled structural steel plates, strips, and long products. S355J2 is the most common structural steel grade (fy = 355 MPa). When specifying: always provide the full designation including grade (e.g., IPE300 S355J2H), length, and quantity. Consider minimum order quantities — small quantities may require cutting from stock lengths.

Section	I (cm⁴)	Z (cm³)
IPE 100	171	34.2
IPE 120	318	53
IPE 140	541	77.3
IPE 160	869	109
IPE 180	1,320	146
IPE 200	1,943	194
IPE 220	2,772	252
IPE 240	3,892	324
IPE 270	5,790	429
IPE 300	8,356	557
IPE 330	11,770	713
IPE 360	16,270	904
IPE 400	23,130	1160
IPE 450	33,740	1500
IPE 500	48,200	1930

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