Comprehensive Notes – Stability & Strength of Structures

ST 1 – Strength of Materials and Mechanics

• Strength of materials = branch of mechanics analyzing stresses, strains, stability in deformable bodies.
• Mechanics split: Kinematics, Statics, Dynamics.
• Goals: ensure constructions are strong, stiff, stable, durable, economical.
• Key properties considered: material nature, deformation, stress distribution; formulas derived to size elements.

ST 2 – Loads & Forces

Definitions

• Force (F) is vector with magnitude, direction, sense, application point; unit NEWTON (N).
• $F=m\,a$ ; Weight $F=m\,g$ with $g\approx9.81\,m/s^2$.
• Moment: $M=F\,\text{arm}$; types: bending (Mb), torsion (Mt). Units Nm.

Types of Loads

1. Concentrated (point).
2. Uniformly distributed (line/area).
3. Non-uniform.

External vs Internal

• External loads: dead weight, live, wind, snow, seismic, water/soil, thermal, fire, impact.
• Internal forces: inertia within the member resisting external loads; produce stresses (normal, shear) and deformations.

Resultant, Composition & Decomposition

• Multiple forces replaced by single resultant via parallelogram rule.
• Decompose an inclined force into vertical & horizontal (e.g., arch thrust).

Equilibrium Equations

• ∑Fx=0, ∑Fy=0, ∑M=0.
• Supports: fixed (clamp), pin, roller. Number of reactions 3,2,1 respectively.

Stability Example

• 70 m office tower, wind 12 740 kN (2 % exceedance). Dead load 27 000 kN. No overturning: resultant within base.

ST 3 – Material Properties

Common Structural Materials

• Steel (S235, S355, etc.).
• Aluminium, concrete (normal & light), wood, masonry, polymers.

Key Properties & Phenomena

• Weight (density, unit weight).
• Strength (tension/compression); σ=F/A.
• Modulus E; $\epsilon=\sigma/E$.
• Thermal expansion $\Delta l=\alpha l\Delta T$.
• Shrinkage (concrete, wood), Creep (time-dependent), Fatigue (cyclic), Durability, Fire resistance.

ST 4 – Stresses & Member Actions

Stress Categories

• Normal: tension (σt), compression (σc).
• Bending: combined compression & tension; $σ_{max}=M/W$ with section modulus W.
• Shear: τ = VQ/It (simplified).
• Torsion: shear due to twisting.
• Buckling/knick, lateral-torsional buckling, local plate buckling.

Strength Design

• Ensure $σ<em>{Ed} \leq σ</em>{Rd}$ .
• Limit deformations: deflection, vibration.
• Safety factors: γF on loads (1.2 dead, 1.5 live), γM on material (e.g., 1.0 steel).
• Consequence classes CC1–CC3 adjust γ.

ST 5 – Global Stability

• Buildings must resist horizontal actions (wind, seismic) via stable systems: frames, shear walls (schijven), braced bays.
• Stabiliteitsvlakken types: Raamwerk (moment frame), Schijf (solid wall/diaphragm), Vakwerk (bracing).
• Hallen: choose among hinged frames + roof bracing, rigid column bases, knee frames, etc.

ST 6 – Stiffness & Serviceability

• Deformations: axial, bending deflection $f=\frac{5q l^4}{384EI}$ (simple beam).
• Sources: load, temperature, shrinkage, creep, settlement.
• Criteria: Δ ≤ L/250 (strength), L/300–500 (finishes), vibration limits (f > 4 Hz typical).

ST 7 – Durability

• Prevent corrosion (coatings, cover), freeze-thaw, chemical attack.
• Fire: steel loses half yield at 400–600 °C; concrete spalls; wood chars but maintains core.

ST 8–9 – Soil Mechanics & Foundations

Soil Types & Properties

• Sand/gravel (non-cohesive, good drainage), clay/leem (cohesive), veen (organic), man-made fill.
• Determine via CPT (cone resistance q_c), boringen, groundwater level.
• Bearing capacity depends on c, φ, γ: $\tau=c+σ\tan φ$.

Loads to Foundations

• Dead 75 %, prestress, live, water, wind, seismic.

Foundation Forms

1. Shallow (on staal): strips, pads, raft. Minimum embedment 0.8 m frost.
2. Deep: piles (prefab, cast-in-place), caissons; rely on end bearing + skin friction.
3. Raft with stiffening ribs.

Settlements

• Immediate + consolidation; differential causes cracks; control by larger footing, soil improvement, reduce load.

ST 10 – Concrete Structures

Composition

• Cement + water (w/c ≤ 0.5), aggregates 70 % vol., admixtures.
• Strength classes C20/25 … C100/115.

Reinforced Concrete

• Steel bars (BE500) resist tension; cover c_min for durability/fire.
• Design: provide main, secondary, shear (stirrups), anchorage L_b.

Prestressed Concrete

• Pre-tensioned (factory) or post-tensioned (tendon ducts); induce compression to counter service tension.

Elements

• Footings, columns, beams, slabs (one-way, two-way, ribs), walls, stairs, balconies.
• Detailing: column shoes, shear keys, punching shear reinforcement, construction joints.

ST 11 – Steel Structures

Steel Grades & Shapes

• S235, S275, S355; hot-rolled profiles HEA/B/M, IPE, UNP, angles, tubes; cold-formed sections.

Design Checks

• Axial, bending, shear, combined; lateral-torsional buckling; section classification (1–4).
• Fire protection: intumescent paint, boards, concrete encasement.

Connections

• Bolted (friction/slip, bearing), welded, castellated beams, column base plates.

ST 12 – Floor Systems

Categories

1. Wooden joists.
2. Beam-block (balken/potten).
3. Precast hollow core (welfsels).
4. In-situ RC slabs (solid, rib, waffle, flat plate, T & TT).
5. Semi-precast/breedplaat (predal) with in-situ topping.
6. Steel deck composite.

Detailing

• Legplan: numbering, spans, supports.
• Opleg length: ≥ h/2, min 70 mm (concrete) or 100 mm (masonry).
• Topping: ≥ 30 mm, C25/30, mesh 150×150 Ø5.
• Joints: grout key, shear ties, continuity reinforcement.

ST 13 – Cracks & Forensic

Causes

• Differential settlement, thermal/shrinkage, overload, point reactions, vibration, moisture changes, foundation heave, tree roots, groundwater lowering.
• Diagnose with plaster "getuigen" or gauge plates; track width.

Patterns

• 45° from point load, vertical due to wall shrinkage, diagonal at openings, horizontal at floor line.
• Remedies: structural joints, reinforcement, underpinning, drainage.

ST 14 – Stability Drawings & Workflow

1. Simplify architect plans to structural skeleton; define bearing walls, beams, slabs, columns.
2. Dimension using tables (span/depth ~ 1/15 etc.).
3. Number elements (B beams, K columns, FB footing, W walls).
4. Engineer reviews, iterates; produces reinforcement drawings:
   • Bars labeled (A, B, …), notation 2Ø20(2A), stirrups bgØ8 @ 15 cm.
5. Produce schedules: steel list, bar bending, concrete volumes.