Design for Strength and Stiffness

Author

Professor. Hisham Ibrahim

Design for Strength and Stiffness

Summary

A vehicle’s structure must ensure safety (crash resilience) and comfort (vibration control), requiring strength (resistance to permanent deformation) and stiffness (resistance to elastic deformation). Stress types—normal, shear, and bending—are managed through designs like Space Frames (axial loads) or Body-on-Frame (bending/shear). Stiffness affects handling, solidness, and NVH, measured via tests (e.g., H-point bending). Torsional stiffness, critical yet challenging (due to localized loads), depends on structural design, closed sections, and joint rigidity.

Learning Objectives

  • Define the concepts of strength and stiffness as essential requirements for vehicle design.

  • Explain the different types of stress that vehicle structures encounter, including normal, shear, and bending.

  • Compare how Space Frame and Body-on-Frame architectures inherently manage and distribute loads.

  • Analyze the factors that influence a vehicle’s bending and torsional stiffness, such as Young’s modulus, moment of inertia, and structural configuration.

  • Interpret typical bending and torsional stiffness values for various vehicle types and discuss their implications for performance.

Design Objective

A well-engineered vehicle must ensure safety and comfort during normal operation and crash events. Crashworthiness involves absorbing impact energy and minimizing intrusion. Comfort requires vibration-free operation and structural integrity.

Structural Design Requirements

Strength and stiffness are essential:

  • Strength : Resistance to permanent deformation

  • Stiffness : Resistance to elastic deformation

Strength

Stress depends on load magnitude, geometry, and dimensions. Types of stress:

  1. Normal : Tensile and compressive

  2. Shear : Transverse and torsional

  3. Bending : Curvature-induced tension and compression

Architectural Influence

  • Space Frame : Truss elements carry axial loads

  • Body-on-Frame : Ladder frame resists bending; joints transmit shear

Stiffness

Stiffness affects:

  • Handling

  • Perception of solidness

  • Vibration performance

  • Functionality

Bending Stiffness

\[\[\begin{equation} \omega_n = \frac{22.4}{\sqrt{48}} \left( \frac{l}{L} \right)^{3/2} \sqrt{\frac{K}{M}} \label{eq:bending-frequency} \end{equation}\]\] \[\[\begin{equation} K = \frac{48EI}{l^3} \end{equation}\]\]

Where:

  • \(_n\): Desired bending frequency

  • \(L\): Vehicle length

  • \(E\): Young’s modulus

  • \(I\): Moment of inertia

  • \(K\): Bending stiffness

  • \(l\): Wheelbase

  • \(M\): Rigidly mounted mass

Measurement

H-point bending test measures stiffness and strength. Load-deflection curves define stiffness. Permanent deformation indicates strength.

Component Contributions

  • Side frame: Hinges, pillars, roof rails

  • Joint stiffness: Critical to overall performance

Target Values

Typical bending stiffness for midsize vehicles: 7000 N/mm

Torsional Stiffness

Defined as: \[\[\begin{equation} T_{\text{max}} = P_{\text{axle}} \cdot \frac{B}{2} \end{equation}\]\] \[\[\begin{equation} T_{\text{max}} = K_{\text{Total}} \cdot \theta, \quad \theta = \frac{H}{B} \end{equation}\]\] \[\[\begin{equation} K_{\text{Total}} = \frac{P_{\text{axle}} \cdot B^2}{2H} \end{equation}\]\]

Typical Values

  • Space frame: 1000–2000 Nm/deg

  • Body-on-frame: 2000–6000 Nm/deg

  • Passenger cars: 7000–15000 Nm/deg

  • Luxury cars: 13000–20000+ Nm/deg

Influencing Factors

  1. Structural configuration (monocoque vs. body-on-frame)

  2. Closed sections and surfaces

  3. Special configurations (convertibles, backbone frames)

  4. Joint flexibility and continuity

  5. Optimization (strain energy, mass distribution)

Comparison

Torsional stiffness is more challenging than bending due to localized loads.