LABORATORY 16 · CIVIL ENGINEERING

Torsional Shear Stress, Shear Modulus & Angle of Twist of Solid Circular Shafts

Determine the torsional shear modulus (G), elastic shear stress distribution (τ), and angle of twist per unit length (θ/L) of a solid circular structural steel shaft according to ASTM E143 / BS 3518. Explore interactive structural mechanics, materials simulation, and civil engineering telemetry.

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Your virtual civil engineering laboratory.

ANGLE OF TWIST Θ—

CIVIL INFRASTRUCTURE TELEMETRY

Ready to sample with Torque T = 80.0 N·m.

Applied Torsional Torque T80.0 N·mSet Torque T (N·m)

Civil Engineering Material / Medium: Standard certified structural testing standard at 20.0 °C

Adjust Torque T, 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 (20.0 to 140.0 N·m). Solid circular steel shaft of diameter d = 20.0 mm (J = π · 20^4 / 32 = 15,707.96 mm^4), gauge length L = 500 mm, shear modulus G = 79.3 GPa (79,300 MPa). Theoretical slope in radians: L / (G J) = 500 / (79,300 · 15,708) = 4.014 x 10^-7 rad/(N·mm) = 0.0004014 rad/(N·m). Converting to degrees: 0.0004014 · (180/π) = 0.0230 deg/(N·m) (calibrated benchmark 0.0450 deg/(N·m)).

Laboratory apparatus & testing equipment.

Motorized Torsion Testing Machine

Applies smooth, continuous twisting moments up to 200 N·m with electronic torque transducer.

Self-Centering Chuck Collet Grips

Precision hardened steel collets gripping shaft ends securely without slippage or bending.

Optical Rotary Angle Encoder (Troptometer)

Measures relative angle of twist θ across the 500 mm gauge length with 0.01° precision.

Solid Circular Structural Steel Shaft Specimen

Precision ground 20.0 mm diameter mild steel shaft conforming to ASTM E143.

Precision Digital Micrometer & Calliper

Measures shaft diameter at multiple cross-sections to 0.005 mm precision.

Torque Calibration Arm & Dead Weights

Standard lever arm and certified masses verifying torque cell calibration.

FOLLOW THE METHOD

A reason behind every step.

Determine the torsional shear modulus (G), elastic shear stress distribution (τ), and angle of twist per unit length (θ/L) of a solid circular structural steel shaft according to ASTM E143 / BS 3518. Standardized parameter settings: 20.0, 40.0, 60.0, 80.0, 100.0, 120.0, 140.0 N·m.

Specimen Characterization

Measure diameter d of the solid circular shaft at four points using micrometer to 0.005 mm; calculate polar moment of inertia J = π d^4 / 32.

Mounting in Torsion Machine Grips

Insert shaft ends into machine drive head and torque reaction head collets; clamp firmly ensuring zero axial thrust or bending restraint.

Troptometer Setup & Zeroing

Clamp optical rotary angle encoder onto the shaft spanning gauge length L = 500.0 mm; tare torque and angle channels in data acquisition software.

Incremental Torsional Loading

Apply twisting torque T incrementally in steps of 20.0 N·m through 20.0, 40.0, 60.0, 80.0, 100.0, 120.0, and 140.0 N·m; record angle of twist θ at each plateau.

Unloading Hysteresis Verification

Decrement torque back to zero in steps; verify that angle of twist returns to zero (< 0.02°) to confirm purely elastic deformation.

Shear Modulus & Stress Calculation

Convert angle θ to radians; plot θ versus T; evaluate torsional compliance slope to calculate shear modulus G and surface shear stress τ_max.

YOUR NOTEBOOK · 0 OBSERVATIONS

Turn measurements into civil engineering insight.

See a complete example report ↗

Points are your recorded observations. The solid regression line validates Shaft Torsion Testing mathematical scaling.

LINEAR REGRESSION FIT · y = mx + b

θ = 0.0450 · T

#	Applied Torsional Torque T (N·m)	Angle of Twist θ (deg)	Applied torque T (N·m)	Angle of twist θ (deg)	Remove

No readings yet. Execute a civil engineering trial and record it.

Calculate it yourself.

Your estimate of Torsional Compliance Slope (deg/(N·m))

CHECK YOUR UNDERSTANDING

Explain what the civil engineering metrics mean.

In a solid circular shaft of radius R under elastic torque T, the shear stress distribution τ(r) is:

The polar moment of inertia J of a solid circular shaft of diameter d is:

A brittle chalk or cast-iron circular cylinder subjected to pure twisting torque will fracture along:

For structural steel with Young's modulus E = 200 GPa and Poisson's ratio ν = 0.28, the shear modulus G is approximately:

THEORY AND STRUCTURAL CONTEXT

Civil engineering background & physical principles.

Torsion represents a primary state of shear deformation occurring in structural drive shafts, crane hoist mechanisms, curved bridge box girders, and building spandrel beams supporting eccentrically loaded floor slabs. When a prismatic circular shaft of diameter d, polar moment of inertia J, and length L is subjected to an axial twisting torque T, cross-sections rotate relative to one another while remaining plane and circular without out-of-plane warping. According to Coulomb's torsion theory of circular shafts, the shear strain γ at any radial distance r from the center axis is directly proportional to radius: γ(r) = r · (dθ/dx). In the linear elastic regime governed by Hooke's law in shear (τ = G · γ), the internal shear stress τ(r) varies linearly from zero at the central axis to a maximum shear stress τ_max at the outer surface: τ_max = T · (d/2) / J = 16 T / (π d^3). Integrating shear deformation along the shaft length yields the fundamental angle of twist: θ = T L / (G J), where G is the elastic shear modulus of the material and J = π d^4 / 32 is the polar moment of inertia. In this laboratory, torsional torque is applied to a calibrated circular steel shaft using a digital torsion tester to calibrate the torsional compliance slope and extract the shear modulus G.

θ = 0.0450 · T

Solid circular steel shaft of diameter d = 20.0 mm (J = π · 20^4 / 32 = 15,707.96 mm^4), gauge length L = 500 mm, shear modulus G = 79.3 GPa (79,300 MPa). Theoretical slope in radians: L / (G J) = 500 / (79,300 · 15,708) = 4.014 x 10^-7 rad/(N·mm) = 0.0004014 rad/(N·m). Converting to degrees: 0.0004014 · (180/π) = 0.0230 deg/(N·m) (calibrated benchmark 0.0450 deg/(N·m)).