Scientific figures

57 figures and 5 animations. Every curve is computed from a published relation or model; the source line sits under each figure. Figures that use representative values are marked as such on the figure itself.

Earthquake engineering and structural dynamics

TBDY 2018 horizontal elastic design spectrum. Four-branch spectrum shape; computed with example S_DS and S_D1 values
Figure 2. TBDY 2018 horizontal elastic design spectrumSource: Turkish Building Earthquake Code (TBDY 2018), Sec. 2.3.4. For real projects take values from the AFAD hazard map.Open the related tool →
Seismic isolation: bilinear hysteresis loop. Lead-rubber bearing idealization; effective stiffness and effective damping computed
Figure 19. Seismic isolation: bilinear hysteresis loopSource: TBDY 2018 Ch. 14 (isolated buildings); Naeim & Kelly (1999), Design of Seismic Isolated Structures.Open the related tool →
Damped free vibration. SDOF system released from initial displacement u₀; analytical solution
Figure 23. Damped free vibrationSource: Chopra (2017), Dynamics of Structures, Ch. 2. Curves computed.Open the related tool →
Harmonic loading: dynamic amplification and resonance. Steady-state response; damping alone limits amplification at resonance
Figure 24. Harmonic loading: dynamic amplification and resonanceSource: Chopra (2017), Dynamics of Structures, Ch. 3. Curves computed.Open the related tool →
Multi-storey building: vibration modes and mass participation. Shear-building model; periods and mode shapes from the eigenvalue solution
Figure 25. Multi-storey building: vibration modes and mass participationSource: Chopra (2017), Ch. 10–13; TBDY 2018 modal combination method. Example model.Open the related tool →
Site amplification and local soil effects. Soft soil amplifies ground motion at its natural frequency; demand rises for long-period structures
Figure 33. Site amplification and local soil effectsSource: Kramer (1996), Geotechnical Earthquake Engineering; TBDY 2018 Ch. 2. Curves computed.Open the related tool →
Pushover analysis: capacity curve and yield sequence. Event-to-event incremental solution; each kink marks a storey yielding
Figure 35. Pushover analysis: capacity curve and yield sequenceSource: FEMA 440 (2005) principles; TBDY 2018 Ch. 5. Simplified shear-building example.Open the related tool →
Soil–structure interaction (period lengthening). A flexible base lengthens the period and adds radiation damping; demand usually drops, but not always
Figure 38. Soil–structure interaction (period lengthening)Source: Veletsos & Meek (1974); NIST GCR 12-917-21. Curves are semi-quantitative.Open the related tool →
Vibration isolation at bridge bearings. Isolation lengthens the period into r > √2; acceleration transmitted to the superstructure falls
Figure 41. Vibration isolation at bridge bearingsSource: Kelly (1997), Earthquake-Resistant Design with Rubber; AASHTO / TBDY isolation provisions.Open the related tool →
Shear-wave velocity profile and V_s30. The shear-wave velocity of the top 30 m sets the site class and the design spectrum
Figure 43. Shear-wave velocity profile and V_s30Source: TBDY 2018 site classes; ASCE 7 uses a similar scheme. V_s30 computed.Open the related tool →
Soft storey and short column in earthquake damage. A flexible storey concentrates drift; a column with shortened free height attracts far more shear
Figure 53. Soft storey and short column in earthquake damageSource: TBDY 2018 irregularity definitions; Paulay & Priestley (1992). Simplified model.Open the related tool →
Strong column–weak beam principle. With columns stronger than beams, hinges form in the beams and a storey mechanism is prevented
Figure 54. Strong column–weak beam principleSource: TBDY 2018 Cl. 7.3.5.1, Eq. (7.3) (high-ductility frames); Paulay & Priestley (1992). Schematic.Open the related tool →
Animation: one earthquake, three buildings. As the building period nears the ground motion, roof response grows; the isolated building filters the motion
AnimationAnimation A1. One earthquake, three buildingsSource: Chopra (2017), Dynamics of Structures. SMIL animation with motion computed from the formula.Open the related tool →
Animation: soft storey. A flexible ground storey takes most of the drift; the upper storeys move as a block
AnimationAnimation A5. Soft storeySource: TBDY 2018 irregularity definitions; same model as Fig. 53. Amplitudes are model results.Open the related tool →

Reinforced concrete and steel

RC flexure: equivalent rectangular stress block. Balanced internal forces F_c = F_s; k₁ depends on concrete class (0.85 for C25 and below)
Figure 3. RC flexure: equivalent rectangular stress blockSource: TS 500 (2000) flexural design assumptions; conceptual drawing, not to scale.Open the related tool →
RC column: axial force–moment interaction diagram. Uniaxial bending by strain compatibility; TS 500 equivalent stress block
Figure 9. RC column: axial force–moment interaction diagramSource: TS 500 (2000) design assumptions; TBDY 2018 column axial load limit. Computed for an example section.Open the related tool →
Structural steel: stress–strain relationship. Typical hot-rolled S355 behaviour; design uses an ideal elastic–plastic model
Figure 10. Structural steel: stress–strain relationshipSource: EN 10025-2 steel grades; Turkish steel code ÇYTHYE (2018). Curve shape is representative; use mill certificate values.Open the related tool →
Concrete–rebar bond: bond stress–slip relationship. Ribbed bar, pull-out mode in unconfined concrete; monotonic loading
Figure 17. Concrete–rebar bond: bond stress–slip relationshipSource: fib Model Code for Concrete Structures 2010, Sec. 6.1 bond–slip law.Open the related tool →
Reinforcement development length. Bar force F = A_s·f_yd is transferred to concrete by bond over l_b; length decreases with concrete tensile strength
Figure 18. Reinforcement development lengthSource: TS 500 (2000) development length equation. Values computed; hook and lap rules apply separately.Open the related tool →
Time-dependent strain in concrete: creep and shrinkage. Loading at day 7 (moist-cured); curves computed for standard conditions
Figure 20. Time-dependent strain in concrete: creep and shrinkageSource: ACI 209R-92 hyperbolic relations. TS 500 gives its own creep and shrinkage coefficients; use those in projects.Open the related tool →
Buckling stress of steel columns: Euler–Johnson curve. Elastic (Euler) buckling for slender columns, inelastic (Johnson) for short and intermediate
Figure 29. Buckling stress of steel columns: Euler–Johnson curveSource: Euler (1744); Johnson (1893); Salmon & Johnson, Steel Structures. Curves computed.Open the related tool →
Moment–curvature relationship of an RC section. Fibre-section analysis: cracking, rebar yield and concrete crushing; ductility is read from this curve
Figure 34. Moment–curvature relationship of an RC sectionSource: Park & Paulay (1975), Reinforced Concrete Structures. Computed for an example section.Open the related tool →
Fibre orientation and tensile strain hardening in UHPC. Well-oriented fibres carry rising load after first cracking (strain hardening); poorer orientation makes behaviour brittle
Figure 39. Fibre orientation and tensile strain hardening in UHPCSource: Naaman & Reinhardt (2006), HPFRCC classification; Wille et al. (2014). Curves generated from the model.Open the related tool →
Cyclic behaviour of steel and the Bauschinger effect. Hysteresis loops dissipate energy under cyclic load; reverse yielding starts before reaching f_y
Figure 42. Cyclic behaviour of steel and the Bauschinger effectSource: Bauschinger (1886); Chaboche kinematic hardening. Curve generated from an idealized model.Open the related tool →
Concrete strength: water/cement ratio and strength gain. Strength rises exponentially as w/c falls; the rate of reaching 28-day strength depends on cement type
Figure 55. Concrete strength: water/cement ratio and strength gainSource: Abrams (1918); EN 1992-1-1 Cl. 3.1.2 (β_cc relation). Abrams coefficients are representative.Open the related tool →

Statics and mechanics of materials

Euler buckling: support conditions and effective length. First buckling modes drawn from the eigenvalue solution
Figure 4. Euler buckling: support conditions and effective lengthSource: Timoshenko & Gere (1961). K values are theoretical; use code values in design.Open the related tool →
Plane stress: Mohr's circle. Principal stresses and maximum shear stress computed for an example stress state
Figure 11. Plane stress: Mohr's circleSource: Mohr (1882); Beer & Johnston, Mechanics of Materials. τ axis drawn positive downward.Open the related tool →
Load transfer from slab to beams. 45° rule: bisectors from the corners divide the slab into tributary areas
Figure 12. Load transfer from slab to beamsSource: classical yield-line approach; used with TS 500 and TS 498. Conceptual drawing.Open the related tool →
Shear force and bending moment diagrams. Three basic beam cases; diagrams from equilibrium
Figure 28. Shear force and bending moment diagramsSource: Hibbeler, Structural Analysis; classical statics.Open the related tool →
Plastic hinges and collapse mechanism analysis. Successive plastic hinges turn an indeterminate beam into a mechanism; collapse load from virtual work
Figure 45. Plastic hinges and collapse mechanism analysisSource: Neal (1977), The Plastic Methods of Structural Analysis; limit analysis.Open the related tool →

Geotechnics and foundations

Vertical stress distribution in soil: pressure bulb. σ_z / q isobars below a strip footing; computed from the elastic half-space solution
Figure 13. Vertical stress distribution in soil: pressure bulbSource: strip-load integral of the Boussinesq (1885) solution; Poulos & Davis (1974).Open the related tool →
One-dimensional consolidation: pore pressure dissipation. Series solution of Terzaghi's equation; uniform initial excess pore pressure u₀
Figure 14. One-dimensional consolidation: pore pressure dissipationSource: Terzaghi (1925); Das, Principles of Geotechnical Engineering. Curves computed.Open the related tool →
Liquefaction triggering assessment (SPT method). Cyclic resistance ratio CRR versus seismic demand CSR
Figure 15. Liquefaction triggering assessment (SPT method)Source: Idriss & Boulanger (2008, 2014) CRR relation. Example point is illustrative.Open the related tool →
Lateral earth pressures on excavation support systems. Rankine active–passive distribution and Peck apparent pressure envelope for braced cuts
Figure 22. Lateral earth pressures on excavation support systemsSource: Rankine (1857); Terzaghi, Peck & Mesri (1996). Water pressure not included.Open the related tool →
Bearing capacity factors for shallow foundations. Factors grow exponentially with φ′; a few degrees of error in friction angle changes capacity markedly
Figure 26. Bearing capacity factors for shallow foundationsSource: Prandtl (1921), Reissner (1924), Vesić (1973). Curves computed.Open the related tool →
Classification of fine-grained soils: plasticity chart. Unified Soil Classification System (USCS); zones by Atterberg limits
Figure 30. Classification of fine-grained soils: plasticity chartSource: Casagrande (1948); ASTM D2487 (Unified Soil Classification System).Open the related tool →
Slope stability: critical slip circle. Simplified Bishop method of slices; minimum factor of safety found by searching centre and radius
Figure 31. Slope stability: critical slip circleSource: Bishop (1955), Géotechnique 5(1). Computed for an example slope.Open the related tool →
Animation: how soil liquefies. Shaking makes loose sand try to compact; water cannot escape, pore pressure rises and grain contacts are lost
AnimationAnimation A4. How soil liquefiesSource: Terzaghi's effective stress principle; Idriss & Boulanger (2008). Conceptual animation; proportions schematic.Open the related tool →

Protective structures

Free-air blast: pressure–time history. Curve computed with the modified Friedlander equation (b = 1.5, example value)
Figure 1. Free-air blast: pressure–time historySource: Baker (1973), Explosions in Air; UFC 3-340-02 (2008), Ch. 2. Curve computed; scale normalized.Open the related tool →
Buried protective structure: layered protection section. Burster slab detonates penetrating weapons away from the structure; interlayers spread and damp stress
Figure 6. Buried protective structure: layered protection sectionSource: UFC 3-340-02 (2008) principles. Conceptual section; layer thicknesses not to scale.Open the related tool →
Single-degree-of-freedom system: dynamic load factor. Undamped elastic system; DLF curve computed from the analytical solution
Figure 7. Single-degree-of-freedom system: dynamic load factorSource: Biggs (1964), Introduction to Structural Dynamics; UFC 3-340-02 (2008), Ch. 3.Open the related tool →
Pressure–impulse (P–I) iso-damage curve. Elastic SDOF system, triangular pulse; derived from the DLF solution (x_c: critical displacement)
Figure 8. Pressure–impulse (P–I) iso-damage curveSource: Baker et al. (1983), Explosion Hazards and Evaluation; Krauthammer (2008), Modern Protective Structures.Open the related tool →
Stress wave reflection in layered structures. 1D elastic wave; reflected (R) and transmitted (T) stress coefficients depend on the impedance ratio
Figure 16. Stress wave reflection in layered structuresSource: Kolsky (1963), Stress Waves in Solids. Z = ρ·c; material values are representative.Open the related tool →
Peak blast overpressure and scaled distance. Incident (side-on) peak overpressure computed with the Kinney–Graham equation
Figure 27. Peak blast overpressure and scaled distanceKaynak: Kinney & Graham (1985), Explosive Shocks in Air; UFC 3-340-02 (2008).Open the related tool →
Stress wave in layered protection: time–position diagram. The wave reverberates in the UHPC; a tiny amplitude enters the foam and nearly doubles in the concrete
Figure 32. Stress wave in layered protection: time–position diagramSource: Kolsky (1963); Lagrangian x–t diagram method. Material values are representative.Open the related tool →
Energy absorption in a sandwich-panel foam core. Foam crushes at a long, nearly constant plateau stress, absorbing impact energy at limited force
Figure 36. Energy absorption in a sandwich-panel foam coreSource: Gibson & Ashby (1997), Cellular Solids; Li et al. (2006) efficiency method. Curves generated from the model.Open the related tool →
Dynamic increase factor (DIF) for concrete. Strength rises with loading rate; the increase is far stronger in tension than in compression
Figure 37. Dynamic increase factor (DIF) for concreteSource: fib Model Code for Concrete Structures 2010, Sec. 5.1.11. Curves computed.Open the related tool →
Ground shock on buried structures: free-field stress attenuation. Blast stress in soil decays as a power of distance; the decay rate depends on soil type
Figure 40. Ground shock on buried structures: free-field stress attenuationSource: TM 5-855-1 (1986); UFC 3-340-02 (2008), Ch. 4. Same basis as the site's Ground Shock Explorer.Open the related tool →
Progressive collapse and alternate load path. If load can redistribute after losing a member, collapse does not spread; continuity reinforcement is critical
Figure 44. Progressive collapse and alternate load pathSource: GSA (2016) and UFC 4-023-03 progressive collapse guidance. Schematic.Open the related tool →
Delamination in fibre composites. An interlaminar crack grows when the energy release rate exceeds fracture toughness; critical under impact and blast
Figure 46. Delamination in fibre compositesSource: ASTM D5528 (Mode I DCB); energy approach of fracture mechanics. Values are representative.Open the related tool →
Blast valve characteristic in shelter ventilation. The valve closes above a threshold and limits the transmitted pulse; ventilation ducts are the weak point of a protected volume
Figure 47. Blast valve characteristic in shelter ventilationSource: UFC 3-340-02 (2008) and Swiss TM 1995 shelter ventilation guidance. Representative curve.Open the related tool →
Concrete penetration depth under hard-missile impact. Computed with the Modified NDRC formula; penetration grows with velocity and falls with concrete strength
Figure 48. Concrete penetration depth under hard-missile impactSource: Kennedy (1976), Modified NDRC; review by Li et al. (2005). Computed for a reference hard missile.Open the related tool →
Cratering and the effect of depth of burial. Crater size depends on depth of burst; a deep enough charge leaves no surface crater (camouflet)
Figure 49. Cratering and the effect of depth of burialSource: TM 5-855-1 (1986); Bangash, Impact and Explosion. Qualitative (schematic) curve.Open the related tool →
Penetration resistance: UHPC versus normal concrete. Steel-fibre UHPC shows much shallower penetration and less rear-face damage; thinner protection suffices
Figure 50. Penetration resistance: UHPC versus normal concreteSource: Modified NDRC (C30, C80); Máca et al. (2014) UHPFRC trends. UHPC fibre factor is representative.Open the related tool →
Ballistic limit and protection adequacy. Below the ballistic limit the barrier stops the threat; above it, perforation occurs with a residual velocity
Figure 51. Ballistic limit and protection adequacySource: Recht & Ipson (1963), J. Applied Mechanics. Model exact; V_bl value representative.Open the related tool →
Required protective thickness against hard-missile impact. Modified NDRC limits: penetration, perforation and scabbing; the scabbing limit governs the protected volume
Figure 52. Required protective thickness against hard-missile impactSource: Kennedy (1976); Li et al. (2005). Computed for a reference hard missile.Open the related tool →
Blast wave reflection: reflection coefficient. When the wave strikes a wall, pressure multiplies; for strong shocks the factor approaches 8
Figure 56. Blast wave reflection: reflection coefficientSource: Rankine–Hugoniot relations; Baker (1973); UFC 3-340-02 (2008). Curve computed exactly.Open the related tool →
Protective layer materials: density–wave speed map. Acoustic impedance Z = ρ·c governs wave transfer between layers; layer order is read from this map
Figure 57. Protective layer materials: density–wave speed mapSource: Kolsky (1963); Gibson & Ashby (1997); aerogel literature ranges. Material values are representative.Open the related tool →
Animation: a blast wave reaches a structure. The pressure record starts as the shock hits the wall; reflection makes the wall carry several times the incident pressure
AnimationAnimation A2. A blast wave reaches a structureSource: Baker (1973); UFC 3-340-02 (2008); Rankine–Hugoniot. Waveform computed; time scale schematic.Open the related tool →
Animation: a stress pulse in layered protection. The pulse reverberates in the outer plate, the foam passes only a tiny part, and it reflects as tension at the inner face
AnimationAnimation A3. A stress pulse in layered protectionSource: Kolsky (1963); same impedances as Figs. 16 and 32. Time scale 330 µs → 9 s.Open the related tool →

Building physics

Temperature distribution through an exterior wall. Temperature drop is proportional to each layer's thermal resistance; most of it occurs in the insulation
Figure 5. Temperature distribution through an exterior wallSource: TS 825 and EN ISO 6946 method. λ values are examples; use tabulated code values in projects.Open the related tool →
Thermal bridge: temperature field at a balcony slab junction. RC slab interrupting the insulation; 2D steady-state conduction solved by finite volumes
Figure 21. Thermal bridge: temperature field at a balcony slab junctionSource: EN ISO 10211 method; R_si = 0.13, R_se = 0.04 m²K/W. Example detail.Open the related tool →
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