75 figures and 9 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.
Interactive charts — change the values yourself
These charts are computed live in your browser. Where the site has a calculation engine (spectrum, bearing capacity, blast) the chart calls it directly; the others are verified closed-form relations.
Figure 64.Sun-path diagram — latitude 40° NSolar altitude and azimuth at the solstices and equinox. Labels: solar timeSource: site solar-geometry engine (Cooper declination); azimuth from south, east −, west + (Duffie & Beckman).Open the related page →Figure 65.Shadow length and building spacing at the winter solsticeShadow length / height on 21 December by solar time; shadows lengthen markedly with latitudeSource: site solar-geometry engine; L = H / tan(α). Terrain slope and neighbouring obstructions not included.Open the related page →Figure 66.Reverberation time: room volume and absorptionT60 for cubic rooms; solid: Sabine, dashed: Eyring. The two converge at low absorptionSource: site acoustics engine — Sabine 0.161V/A, Eyring 0.161V/(−S·ln(1−ᾱ)). Target bands typical (representative).Open the related page →Figure 67.Arch form and the line of thrustThree arches with the same span and rise; the compression-only form depends on how the load is distributedSource: Hooke (1675); Heyman (1969) t/R ≥ 0.107 for a semicircle. Shapes computed in closed form.Open the related page →Figure 68.Stair comfort: riser and goingBlondel relation 2R + G ≈ 63 cm (pace length); escape-stair limits from the regulationSource: Blondel (1675); limits from the Turkish fire code, Art. 41(7) (site escape-stair engine).Open the related page →AnimationAnimation A9.Hooke's inverted chain — from hanging chain to archA hanging chain carries only tension; flipped, the same shape becomes an arch in pure compressionSource: Hooke (1675); catenary y = a·cosh(x/a). Gaudí used hanging-chain models for the Sagrada Família.Open the related page →
Earthquake engineering and structural dynamics
Figure 2.TBDY 2018 horizontal elastic design spectrumFour-branch spectrum shape; computed with example S_DS and S_D1 valuesSource: Turkish Building Earthquake Code (TBDY 2018), Sec. 2.3.4. For real projects take values from the AFAD hazard map.Open the related tool →Figure 19.Seismic isolation: bilinear hysteresis loopLead-rubber bearing idealization; effective stiffness and effective damping computedSource: TBDY 2018 Ch. 14 (isolated buildings); Naeim & Kelly (1999), Design of Seismic Isolated Structures.Open the related tool →Figure 23.Damped free vibrationSDOF system released from initial displacement u₀; analytical solutionSource: Chopra (2017), Dynamics of Structures, Ch. 2. Curves computed.Open the related tool →Figure 24.Harmonic loading: dynamic amplification and resonanceSteady-state response; damping alone limits amplification at resonanceSource: Chopra (2017), Dynamics of Structures, Ch. 3. Curves computed.Open the related tool →Figure 25.Multi-storey building: vibration modes and mass participationShear-building model; periods and mode shapes from the eigenvalue solutionSource: Chopra (2017), Ch. 10–13; TBDY 2018 modal combination method. Example model.Open the related tool →Figure 33.Site amplification and local soil effectsSoft soil amplifies ground motion at its natural frequency; demand rises for long-period structuresSource: Kramer (1996), Geotechnical Earthquake Engineering; TBDY 2018 Ch. 2. Curves computed.Open the related tool →Figure 35.Pushover analysis: capacity curve and yield sequenceEvent-to-event incremental solution; each kink marks a storey yieldingSource: FEMA 440 (2005) principles; TBDY 2018 Ch. 5. Simplified shear-building example.Open the related tool →Figure 38.Soil–structure interaction (period lengthening)A flexible base lengthens the period and adds radiation damping; demand usually drops, but not alwaysSource: Veletsos & Meek (1974); NIST GCR 12-917-21. Curves are semi-quantitative.Open the related tool →Figure 41.Vibration isolation at bridge bearingsIsolation lengthens the period into r > √2; acceleration transmitted to the superstructure fallsSource: Kelly (1997), Earthquake-Resistant Design with Rubber; AASHTO / TBDY isolation provisions.Open the related tool →Figure 43.Shear-wave velocity profile and V_s30The shear-wave velocity of the top 30 m sets the site class and the design spectrumSource: TBDY 2018 site classes; ASCE 7 uses a similar scheme. V_s30 computed.Open the related tool →Figure 53.Soft storey and short column in earthquake damageA flexible storey concentrates drift; a column with shortened free height attracts far more shearSource: TBDY 2018 irregularity definitions; Paulay & Priestley (1992). Simplified model.Open the related tool →Figure 54.Strong column–weak beam principleWith columns stronger than beams, hinges form in the beams and a storey mechanism is preventedSource: TBDY 2018 Cl. 7.3.5.1, Eq. (7.3) (high-ductility frames); Paulay & Priestley (1992). Schematic.Open the related tool →AnimationAnimation A1.One earthquake, three buildingsAs the building period nears the ground motion, roof response grows; the isolated building filters the motionSource: Chopra (2017), Dynamics of Structures. SMIL animation with motion computed from the formula.Open the related tool →AnimationAnimation A5.Soft storeyA flexible ground storey takes most of the drift; the upper storeys move as a blockSource: TBDY 2018 irregularity definitions; same model as Fig. 53. Amplitudes are model results.Open the related tool →
Reinforced concrete and steel
Figure 3.RC flexure: equivalent rectangular stress blockBalanced internal forces F_c = F_s; k₁ depends on concrete class (0.85 for C25 and below)Source: TS 500 (2000) flexural design assumptions; conceptual drawing, not to scale.Open the related tool →Figure 9.RC column: axial force–moment interaction diagramUniaxial bending by strain compatibility; TS 500 equivalent stress blockSource: TS 500 (2000) design assumptions; TBDY 2018 column axial load limit. Computed for an example section.Open the related tool →Figure 10.Structural steel: stress–strain relationshipTypical hot-rolled S355 behaviour; design uses an ideal elastic–plastic modelSource: EN 10025-2 steel grades; Turkish steel code ÇYTHYE (2018). Curve shape is representative; use mill certificate values.Open the related tool →Figure 17.Concrete–rebar bond: bond stress–slip relationshipRibbed bar, pull-out mode in unconfined concrete; monotonic loadingSource: fib Model Code for Concrete Structures 2010, Sec. 6.1 bond–slip law.Open the related tool →Figure 18.Reinforcement development lengthBar force F = A_s·f_yd is transferred to concrete by bond over l_b; length decreases with concrete tensile strengthSource: TS 500 (2000) development length equation. Values computed; hook and lap rules apply separately.Open the related tool →Figure 20.Time-dependent strain in concrete: creep and shrinkageLoading at day 7 (moist-cured); curves computed for standard conditionsSource: ACI 209R-92 hyperbolic relations. TS 500 gives its own creep and shrinkage coefficients; use those in projects.Open the related tool →Figure 29.Buckling stress of steel columns: Euler–Johnson curveElastic (Euler) buckling for slender columns, inelastic (Johnson) for short and intermediateSource: Euler (1744); Johnson (1893); Salmon & Johnson, Steel Structures. Curves computed.Open the related tool →Figure 34.Moment–curvature relationship of an RC sectionFibre-section analysis: cracking, rebar yield and concrete crushing; ductility is read from this curveSource: Park & Paulay (1975), Reinforced Concrete Structures. Computed for an example section.Open the related tool →Figure 39.Fibre orientation and tensile strain hardening in UHPCWell-oriented fibres carry rising load after first cracking (strain hardening); poorer orientation makes behaviour brittleSource: Naaman & Reinhardt (2006), HPFRCC classification; Wille et al. (2014). Curves generated from the model.Open the related tool →Figure 42.Cyclic behaviour of steel and the Bauschinger effectHysteresis loops dissipate energy under cyclic load; reverse yielding starts before reaching f_ySource: Bauschinger (1886); Chaboche kinematic hardening. Curve generated from an idealized model.Open the related tool →Figure 55.Concrete strength: water/cement ratio and strength gainStrength rises exponentially as w/c falls; the rate of reaching 28-day strength depends on cement typeSource: Abrams (1918); EN 1992-1-1 Cl. 3.1.2 (β_cc relation). Abrams coefficients are representative.Open the related tool →Figure 63.Lateral–torsional buckling of steel beamsNominal flexural strength M_n vs unbraced length L_b: yielding, inelastic and elastic zones (C_b = 1, S235)Source: ÇYTHYE 2018 (same structure as AISC 360), site steel-d engine; sections EN 10365, J from numerical solution.Open the related tool →
Statics and mechanics of materials
Figure 4.Euler buckling: support conditions and effective lengthFirst buckling modes drawn from the eigenvalue solutionSource: Timoshenko & Gere (1961). K values are theoretical; use code values in design.Open the related tool →Figure 11.Plane stress: Mohr's circlePrincipal stresses and maximum shear stress computed for an example stress stateSource: Mohr (1882); Beer & Johnston, Mechanics of Materials. τ axis drawn positive downward.Open the related tool →Figure 12.Load transfer from slab to beams45° rule: bisectors from the corners divide the slab into tributary areasSource: classical yield-line approach; used with TS 500 and TS 498. Conceptual drawing.Open the related tool →Figure 28.Shear force and bending moment diagramsThree basic beam cases; diagrams from equilibriumSource: Hibbeler, Structural Analysis; classical statics.Open the related tool →Figure 45.Plastic hinges and collapse mechanism analysisSuccessive plastic hinges turn an indeterminate beam into a mechanism; collapse load from virtual workSource: Neal (1977), The Plastic Methods of Structural Analysis; limit analysis.Open the related tool →
Geotechnics and foundations
Figure 13.Vertical stress distribution in soil: pressure bulbσ_z / q isobars below a strip footing; computed from the elastic half-space solutionSource: strip-load integral of the Boussinesq (1885) solution; Poulos & Davis (1974).Open the related tool →Figure 14.One-dimensional consolidation: pore pressure dissipationSeries solution of Terzaghi's equation; uniform initial excess pore pressure u₀Source: Terzaghi (1925); Das, Principles of Geotechnical Engineering. Curves computed.Open the related tool →Figure 15.Liquefaction triggering assessment (SPT method)Cyclic resistance ratio CRR versus seismic demand CSRSource: Idriss & Boulanger (2008, 2014) CRR relation. Example point is illustrative.Open the related tool →Figure 22.Lateral earth pressures on excavation support systemsRankine active–passive distribution and Peck apparent pressure envelope for braced cutsSource: Rankine (1857); Terzaghi, Peck & Mesri (1996). Water pressure not included.Open the related tool →Figure 26.Bearing capacity factors for shallow foundationsFactors grow exponentially with φ′; a few degrees of error in friction angle changes capacity markedlySource: Prandtl (1921), Reissner (1924), Vesić (1973). Curves computed.Open the related tool →Figure 30.Classification of fine-grained soils: plasticity chartUnified Soil Classification System (USCS); zones by Atterberg limitsSource: Casagrande (1948); ASTM D2487 (Unified Soil Classification System).Open the related tool →Figure 31.Slope stability: critical slip circleSimplified Bishop method of slices; minimum factor of safety found by searching centre and radiusSource: Bishop (1955), Géotechnique 5(1). Computed for an example slope.Open the related tool →AnimationAnimation A4.How soil liquefiesShaking makes loose sand try to compact; water cannot escape, pore pressure rises and grain contacts are lostSource: Terzaghi's effective stress principle; Idriss & Boulanger (2008). Conceptual animation; proportions schematic.Open the related tool →AnimationAnimation A7.How pore pressure brings a slope downAs water rises, effective stress and friction fall; when FS < 1 the mass slides along the circleSource: Bishop (1955), r_u method; same slope and critical circle as Figure 31 (dry FS = 1.81). Circle held fixed.Open the related tool →AnimationAnimation A8.How pore water escapes during consolidationLoad is first carried by the water; as it drains away, excess pore pressure fades and the ground settlesSource: Terzaghi (1925) series solution, double drainage; T_v = c_v·t/H_dr². Same relation as Figure 14.Open the related tool →
Protective structures
Figure 1.Free-air blast: pressure–time historyCurve computed with the modified Friedlander equation (b = 1.5, example value)Source: Baker (1973), Explosions in Air; UFC 3-340-02 (2008), Ch. 2. Curve computed; scale normalized.Open the related tool →Figure 6.Buried protective structure: layered protection sectionBurster slab detonates penetrating weapons away from the structure; interlayers spread and damp stressSource: UFC 3-340-02 (2008) principles. Conceptual section; layer thicknesses not to scale.Open the related tool →Figure 7.Single-degree-of-freedom system: dynamic load factorUndamped elastic system; DLF curve computed from the analytical solutionSource: Biggs (1964), Introduction to Structural Dynamics; UFC 3-340-02 (2008), Ch. 3.Open the related tool →Figure 8.Pressure–impulse (P–I) iso-damage curveElastic SDOF system, triangular pulse; derived from the DLF solution (x_c: critical displacement)Source: Baker et al. (1983), Explosion Hazards and Evaluation; Krauthammer (2008), Modern Protective Structures.Open the related tool →Figure 16.Stress wave reflection in layered structures1D elastic wave; reflected (R) and transmitted (T) stress coefficients depend on the impedance ratioSource: Kolsky (1963), Stress Waves in Solids. Z = ρ·c; material values are representative.Open the related tool →Figure 27.Peak blast overpressure and scaled distanceIncident (side-on) peak overpressure computed with the Kinney–Graham equationSource: Kinney & Graham (1985), Explosive Shocks in Air; UFC 3-340-02 (2008).Open the related tool →Figure 32.Stress wave in layered protection: time–position diagramThe wave reverberates in the UHPC; a tiny amplitude enters the foam and nearly doubles in the concreteSource: Kolsky (1963); Lagrangian x–t diagram method. Material values are representative.Open the related tool →Figure 36.Energy absorption in a sandwich-panel foam coreFoam crushes at a long, nearly constant plateau stress, absorbing impact energy at limited forceSource: Gibson & Ashby (1997), Cellular Solids; Li et al. (2006) efficiency method. Curves generated from the model.Open the related tool →Figure 37.Dynamic increase factor (DIF) for concreteStrength rises with loading rate; the increase is far stronger in tension than in compressionSource: fib Model Code for Concrete Structures 2010, Sec. 5.1.11. Curves computed.Open the related tool →Figure 40.Ground shock on buried structures: free-field stress attenuationBlast stress in soil decays as a power of distance; the decay rate depends on soil typeSource: 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 →Figure 44.Progressive collapse and alternate load pathIf load can redistribute after losing a member, collapse does not spread; continuity reinforcement is criticalSource: GSA (2016) and UFC 4-023-03 progressive collapse guidance. Schematic.Open the related tool →Figure 46.Delamination in fibre compositesAn interlaminar crack grows when the energy release rate exceeds fracture toughness; critical under impact and blastSource: ASTM D5528 (Mode I DCB); energy approach of fracture mechanics. Values are representative.Open the related tool →Figure 47.Blast valve characteristic in shelter ventilationThe valve closes above a threshold and limits the transmitted pulse; ventilation ducts are the weak point of a protected volumeSource: UFC 3-340-02 (2008) and Swiss TM 1995 shelter ventilation guidance. Representative curve.Open the related tool →Figure 48.Concrete penetration depth under hard-missile impactComputed with the Modified NDRC formula; penetration grows with velocity and falls with concrete strengthSource: Kennedy (1976), Modified NDRC; review by Li et al. (2005). Computed for a reference hard missile.Open the related tool →Figure 49.Cratering and the effect of depth of burialCrater size depends on depth of burst; a deep enough charge leaves no surface crater (camouflet)Source: TM 5-855-1 (1986); Bangash, Impact and Explosion. Qualitative (schematic) curve.Open the related tool →Figure 50.Penetration resistance: UHPC versus normal concreteSteel-fibre UHPC shows much shallower penetration and less rear-face damage; thinner protection sufficesSource: Modified NDRC (C30, C80); Máca et al. (2014) UHPFRC trends. UHPC fibre factor is representative.Open the related tool →Figure 51.Ballistic limit and protection adequacyBelow the ballistic limit the barrier stops the threat; above it, perforation occurs with a residual velocitySource: Recht & Ipson (1963), J. Applied Mechanics. Model exact; V_bl value representative.Open the related tool →Figure 52.Required protective thickness against hard-missile impactModified NDRC limits: penetration, perforation and scabbing; the scabbing limit governs the protected volumeSource: Kennedy (1976); Li et al. (2005). Computed for a reference hard missile.Open the related tool →Figure 56.Blast wave reflection: reflection coefficientWhen the wave strikes a wall, pressure multiplies; for strong shocks the factor approaches 8Source: Rankine–Hugoniot relations; Baker (1973); UFC 3-340-02 (2008). Curve computed exactly.Open the related tool →Figure 57.Protective layer materials: density–wave speed mapAcoustic impedance Z = ρ·c governs wave transfer between layers; layer order is read from this mapSource: Kolsky (1963); Gibson & Ashby (1997); aerogel literature ranges. Material values are representative.Open the related tool →AnimationAnimation A2.A blast wave reaches a structureThe pressure record starts as the shock hits the wall; reflection makes the wall carry several times the incident pressureSource: Baker (1973); UFC 3-340-02 (2008); Rankine–Hugoniot. Waveform computed; time scale schematic.Open the related tool →AnimationAnimation A3.A stress pulse in layered protectionThe pulse reverberates in the outer plate, the foam passes only a tiny part, and it reflects as tension at the inner faceSource: Kolsky (1963); same impedances as Figs. 16 and 32. Time scale 330 µs → 9 s.Open the related tool →AnimationAnimation A6.Wave reflection at a free and a fixed endA compressive wave returns as tension from a free end, as compression from a fixed endSource: Kolsky (1963); 1D elastic wave, σ = f(x−ct) ∓ f(2L−x−ct). λ = 0.4L, f_t = 0.4σ₀ representative.Open the related tool →Figure 70.Oblique reflection: angle of incidence and reflection coefficientC_rα = P_rα / P_so; reflection weakens with angle, while Mach reflection raises it at intermediate anglesSource: UFC 3-340-02 Fig. 2-193 (site ufc-oblique-reflection engine); α = 0° values within 3% of Rankine–Hugoniot.Open the related tool →Figure 71.Negative phase: suction pressure versus scaled distanceHemispherical surface burst; the suction that follows the positive phase gains relative weight at long rangeSource: UFC 3-340-02 Fig. 2-16 (site ufc-negative-phase engine). Suction cannot exceed atmospheric (14.7 psi).Open the related tool →Figure 72.Confined explosion: quasi-static gas pressureGas pressure rises with charge mass / free volume; the pressure that fills the room after the shock reflectionsSource: UFC 3-340-02 Fig. 2-152 (site ufc-gas-pressure engine). Venting and openings not included.Open the related tool →Figure 73.Positive phase: pressure and impulse versus scaled distanceHemispherical surface burst (TNT); incident and reflected peak pressure and scaled impulsesSource: UFC 3-340-02 Fig. 2-15 (site ufc-positive-phase engine). Impulses are scaled by W^(1/3).Open the related tool →Figure 74.Air-induced ground shock: soil impedance governsVertical peak particle velocity V = P_so / (ρ·c); for the same blast, soft soil moves far fasterSource: TM 5-855-1 / UFC 3-340-02 (site engines); ρ from Odello Table 3, c mid-range — representative.Open the related tool →Figure 75.Spall and breach thresholds for reinforced concrete wallsBelow these thicknesses the back face spalls or the wall is breached; only the test-data range is drawnSource: UFC 3-340-02 §4-55 (site ufc-spall-breach engine); f′c = 30 MPa, surface burst, C_f = 1.Open the related tool →
Building physics
Figure 5.Temperature distribution through an exterior wallTemperature drop is proportional to each layer's thermal resistance; most of it occurs in the insulationSource: TS 825 and EN ISO 6946 method. λ values are examples; use tabulated code values in projects.Open the related tool →Figure 21.Thermal bridge: temperature field at a balcony slab junctionRC slab interrupting the insulation; 2D steady-state conduction solved by finite volumesSource: EN ISO 10211 method; R_si = 0.13, R_se = 0.04 m²K/W. Example detail.Open the related tool →Figure 58.External wall: insulation thickness and U-valueU = 1 / (R_si + Σd/λ + R_se); horizontal heat flow. Horizontal lines: TS 825:2024 wall limits by climate zoneSource: EN ISO 6946 method; limits TS 825:2024 (site thermal-tr engine). λ values are representative.Open the related tool →Figure 59.Glaser diagram: insulation position decides condensationVapour pressure p and saturation pressure p_s along vapour resistance s_d = μ·d; condensation where p > p_sSource: Glaser method, EN ISO 13788; Magnus p_s. In 20 °C / 50%, out −5 °C / 80%. μ, λ representative.Open the related tool →
Site engineering and loads
Figure 60.Lateral pressure of fresh concrete on formworkColumn form, h = 4 m; faster placement and colder concrete push pressure towards the hydrostatic limitSource: ACI 347R-14 §4.2 (SI), C_w = C_c = 1 (normal concrete, Type I cement, no retarder); 30 kPa ≤ p ≤ ρgh.Open the related tool →Figure 61.Concrete maturity: curing temperature changes strength gainNurse–Saul equivalent age t_e = (T − T₀)/(T_r − T₀)·t, combined with the EN 1992 β_cc(t_e) curveSource: ASTM C1074 (Nurse–Saul); EN 1992-1-1 Cl. 3.1.2. T₀ = −10 °C and s = 0.25 are representative.Open the related tool →Figure 62.Wind: growth of the velocity pressure coefficient with heightK_z by terrain roughness (exposure B, C, D); q_z = 0.613·K_z·K_zt·K_e·V² (Pa)Source: ASCE 7-22 Table 26.10-1 (site asce7-wind engine). Turkish TS 498:2021 profiles differ.Open the related tool →Figure 69.TS 498:2021 wind: stepped velocity pressure with heightTable 4 is stepped; no linear interpolation between bands — the value of the band is usedSource: TS 498:2021 Table 4 (site loads-tr engine); consistent with q = v²/1600. Steep slope: q ≥ 1.1 kN/m².Open the related tool →