Strength Of Materials

Strength of materials, a core discipline in engineering, explores how solid objects respond to different forces and moments. It investigates how materials deform, bend, twist, or fracture under stress, playing a key role in designing safe and efficient structures, machinery, and everyday products. By analyzing properties like elasticity, plasticity, and toughness, this study ensures that materials and structures can endure applied loads without failure, thus protecting both functionality and safety. This field is essential in civil, mechanical, and aerospace disciplines, among others, providing vital insights that drive innovation and reliability in construction and manufacturing.

This dataset and calculations are for educational purposes only .

problem definition

Concrete barriers reinforced with steel rebar are designed to resist impact forces, yet the effectiveness of a single rebar design under high-velocity impact remains to be thoroughly evaluated. This study aims to investigate whether a specific rebar configuration within concrete barriers can effectively halt an object traveling at a given velocity without compromising the barrier's structural integrity. The test will focus on assessing the energy absorption capacity and impact resistance of this single rebar design, providing insight into its suitability for applications requiring enhanced safety in high-impact scenarios.

SET-UP:

Concrete M35
Reinforcing bar 10mm dia, meshed @ 100mm CoC structural steel
Fixed Support: No Dowel bar (free standing)
velocity: 210 m/s (756 km/hr)
Engine Block of a vehicle colliding with concrete barrier. The intent is to use the barriers also for bullet trains.
Duration: 0.001 seconds

INITIAL IMPACT

The initial deformation of concrete barriers upon impact plays a crucial role in determining their effectiveness in high-impact applications. This study focuses on a specific rebar-reinforced concrete barrier design, analyzing how the concrete and embedded steel rebar respond to the forces experienced during the initial moments of impact. By observing the deformation characteristics of the concrete material and rebar at the point of contact, the simulation aims to determine the barrier's ability to absorb and dissipate energy, reducing damage and preventing penetration. Results will inform whether this design offers sufficient protection in scenarios involving high-velocity impacts.

TOTAL DEFORMATION

EQUIVALENT STRESS

EQUIVALENT ELASTIC STRAIN

The damage graph shows a consistent pattern of damage, indicating that the concrete barrier design is not effectively reducing the impact. The velocity probe will provide additional confirmation of this observation.

The time-velocity graph shows that the initial decrease in velocity is due to the impact with the concrete material. However, after this initial impact, the object continues to gain speed. The second peak in the graph corresponds to the impact with the first layer of reinforcing bars, which causes another reduction in velocity. Yet, the velocity rises again, reaching a third peak upon impact with the second layer of reinforcing bars. Over the total observed time, the velocity continues to trend upward, indicating that the concrete barrier was unable to effectively contain or dissipate the impact speed.

The simulation can be viewed in this link: https://youtube.com/shorts/WoxDkWpuw_w?feature=share

IMPACT @ 60 m/s

The initial contact with the concrete material lasted 0.0015 seconds, during which the object maintained a constant speed before the concrete began to absorb the impact over the next 0.0025 seconds. However, examining the velocity trend after the erosion of the concrete material, it’s clear that the impact from the object's speed was not sufficiently mitigated.

Further Work:

The objective is to further improve the design (sensitivity analysis with parameters for size of rebar, position and shape) of the reinforcing bars and concrete material to function like a spring, absorbing the impact energy to a degree that would bring the vehicle to a complete stop by rebounding it thereby preventing potential injury to vehicle passengers. Q.E.D.

DESIGN OF MACHINE MEMBERS

The corrected moment diagram as illustrated from the book Design of Machine Members, 4th Edition by Venton Levy Doughtie and Alex Vallance, p. 189.

Reaction Force 1: Textbook Value : 14000 lb-f, Simulation: 13756 lb-f
Reaction Force 2: Textbook Value : 12000 lb-f, Simulation: 12244 lb-f
Bending Moment at 10000 lb load: Textbook Value : 192000 in-lb, SResult: 95141 in-lb
Bending Moment at 16000 lb load: Textbook Value : 224000 in-lb, SResult: 134760 in-lb

The corrected maximum deflection chart based on total-shear-moment diagram.

KINEMATICS OF RIGID BODIES

Kinematics of rigid bodies deals with the motion of bodies without considering the forces causing the motion. It is a fundamental topic in mechanics that focuses on understanding the position, velocity, and acceleration of points and objects in motion. One intriguing application of rigid body kinematics is the Geneva Wheel mechanism, a device that converts continuous rotary motion into intermittent rotary motion.

Overview of the Geneva Wheel Mechanism

The Geneva wheel, also known as the Maltese cross mechanism, consists of two main components:

Drive Wheel (Driver): A rotating disk with a pin or arm that engages the slotted wheel.
Geneva Wheel (Driven): A slotted wheel with radial slots evenly spaced around its circumference.
As the drive wheel rotates continuously, the pin on the driver engages a slot in the Geneva wheel, causing it to rotate by a fixed angular increment. Between these engagements, the Geneva wheel remains stationary, creating intermittent motion. This mechanism is widely used in film projectors, indexing machines, clocks, and other devices requiring precise, intermittent motion.

Kinematics in the Geneva Mechanism

The Geneva wheel mechanism demonstrates the principles of rigid body kinematics in several ways:

Rotational Kinematics:

The angular displacement, velocity, and acceleration of the Geneva wheel can be analyzed as a rigid body undergoing rotational motion.

The driver pin’s motion defines the kinematic relationship, determining the timing and angle of rotation of the Geneva wheel.

Intermittent Motion:

During engagement, the motion of the Geneva wheel is constrained by the geometry of the slot and the pin, illustrating how rigid body kinematics governs the transfer of motion.

The dwell period, when the Geneva wheel remains stationary, highlights how kinematics can control timing in mechanical systems.

Contact and Constraints:

The interaction between the pin and slot provides a practical example of constrained motion in rigid bodies, where specific contact points dictate the motion path.

Angular Relations and Ratios:

The kinematic relationship between the driver and Geneva wheel depends on the number of slots in the Geneva wheel, dictating the angular step size per rotation of the driver.

Constructed geneva wheel with the designed crank mechanism. The challenge here is to determine the clearance arc depending on the required timing as illustrated in this video. CLICK THIS LINK after so much calculation and drafting as an indexing mechanism found on clocks and watches, automatic packaging, medical equipment, printing press and bottle filling machines.

Velocity Probe of drive pin

Determining the power required to drive the intermittent motion of the geneva wheel at desired 100 rpm.

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