Structural Beam Testing Loading Frame
Rigid steel reaction frame with hydraulic screw jack applying central vertical point loads to 25 kN.
Civil Engineering / Beam Elastic Deflection
FREE TO EXPLORELABORATORY 13 · CIVIL ENGINEERING
Elastic Deflection of Simply Supported Structural Steel Beams & Flexural Rigidity
Verify the Euler–Bernoulli beam flexure theory, measure midspan elastic deflection (δ) under central point loading across span L, and determine the flexural rigidity (EI) of a structural steel beam. Explore interactive structural mechanics, materials simulation, and civil engineering telemetry.
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Your virtual civil engineering laboratory.
MIDSPAN DEFLECTION Δ—
CIVIL INFRASTRUCTURE TELEMETRY
Ready to sample with Load P = 8.0 kN.
Adjust Load P, then execute civil engineering measurement.
Civil engineering telemetry is evaluated rigorously using 64-bit IEEE 754 precision. Residuals reflect ordinary least-squares regression across successive observations. Continuous data structures support high-fidelity structural mechanics and geotechnical continuum modeling.
Civil engineering assumptions and boundary condition limits
The civil engineering physical models apply within the specified calibrated operational window (2.0 to 14.0 kN). Structural steel beam of span L = 1200 mm, moment of inertia I = 4.235 x 10^5 mm^4, E = 200 GPa. Theoretical compliance slope: L^3 / (48 E I) = 1200^3 / (48 · 200,000 · 423,500) = 1.728 x 10^9 / 4.0656 x 10^12 = 0.4250 mm/kN.
Laboratory apparatus & testing equipment.
Pinned and Roller Knife-Edge End Supports
Provides true simply supported boundary conditions (one pinned knife-edge, one sliding roller).
Precision Digital Linear Dial Gauge (LVDT)
Measures beam midspan vertical deflection with 0.001 mm resolution and 25 mm travel.
Calibrated Electronic Load Cell
Measures applied concentrated central load P with 0.01 kN precision.
Precision Steel Beam Specimen
Structural steel rectangular/I-beam with machined straight edges and known cross-sectional geometry.
Precision Metric Vernier Caliper & Tape
Measures span length L, beam width b, and beam depth d to 0.05 mm precision.
FOLLOW THE METHOD
A reason behind every step.
Verify the Euler–Bernoulli beam flexure theory, measure midspan elastic deflection (δ) under central point loading across span L, and determine the flexural rigidity (EI) of a structural steel beam. Standardized parameter settings: 2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0 kN.
01
Beam Dimensions & Section Modulus Measurement
Measure beam cross-sectional width b and depth d at three stations using callipers to 0.05 mm; compute moment of inertia I = b d^3 / 12.
02
Support Setup & Span Alignment
Position pinned support and roller support on the reaction bed; set clear span L = 1200.0 mm using precision rule; place beam centrally on supports.
03
Loading Saddle & Dial Gauge Installation
Mount loading knife-edge saddle at exact midspan (x = 600 mm); position digital dial indicator directly beneath midspan bottom flange; zero the indicator.
04
Pre-Loading & Seating Cycle
Apply a gentle seating load of 1.0 kN to settle knife-edges; release load completely and re-zero dial gauge.
05
Incremental Elastic Loading
Apply central point load incrementally in steps of 2.0 kN through 2.0, 4.0, 6.0, 8.0, 10.0, 12.0, and 14.0 kN; record steady midspan deflection δ at each plateau.
06
Unloading Hysteresis Check
Decrement load in reverse steps back to zero; verify that residual plastic deflection is zero (< 0.02 mm) to confirm true elastic behavior.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into civil engineering insight.
Points are your recorded observations. The solid regression line validates Beam Elastic Deflection mathematical scaling.
LINEAR REGRESSION FIT · y = mx + b
δ = 0.4250 · P
| # | Central Point Load P (kN) | Midspan Deflection δ (mm) | Central point load P (kN) | Midspan deflection δ (mm) | Remove |
|---|
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CHECK YOUR UNDERSTANDING
Explain what the civil engineering metrics mean.
For a simply supported beam of span L with central point load P, midspan deflection is proportional to:
If the depth d of a rectangular beam is doubled while width b remains constant, its deflection under identical load will be:
The slope of the elastic deflection curve dv/dx at the midspan of a symmetrically loaded simply supported beam is:
Flexural rigidity of a structural beam is defined mathematically as the product:
THEORY AND STRUCTURAL CONTEXT
Civil engineering background & physical principles.
In structural civil engineering, the serviceability limit state (deflection control) is just as critical as the ultimate strength limit state. Excessive beam deflections cause unsightly sagging, crack plaster and brittle architectural finishes, jam doors and operable windows, and induce alarming vibrations under human foot traffic. Classical Euler–Bernoulli beam theory dictates that the elastic deflection curve v(x) of a prismatic, homogeneous beam of flexural rigidity EI obeys the fundamental second-order differential equation d^2v/dx^2 = M(x) / (EI), where M(x) is internal bending moment. For a simply supported beam of span L subjected to a concentrated central point load P at midspan (x = L/2), double integration with boundary conditions (zero deflection at supports x = 0 and x = L) yields the famous midspan deflection expression: δ = P L^3 / (48 E I). Measuring midspan deflection δ as a function of load P produces a linear elastic compliance slope C = δ / P = L^3 / (48 E I), from which the experimental flexural rigidity EI and Young's modulus E can be deduced. In this laboratory, a structural steel I-beam is loaded across loads from 2 to 14 kN using digital dial indicators to verify beam flexure theory and evaluate flexural compliance.
δ = 0.4250 · P
Structural steel beam of span L = 1200 mm, moment of inertia I = 4.235 x 10^5 mm^4, E = 200 GPa. Theoretical compliance slope: L^3 / (48 E I) = 1200^3 / (48 · 200,000 · 423,500) = 1.728 x 10^9 / 4.0656 x 10^12 = 0.4250 mm/kN.