Here are the steps to solve this example:
1) Find the moment of inertia, I, of the composite section about the neutral axis:
I = I1 + I2 + A1*d1^2 + A2*d2^2
Where:
I1 = moment of inertia of rectangular section 1 = b1*h1^3/12 = 4*6^3/12 = 144 in^4
I2 = moment of inertia of rectangular section 2 = b2*h2^3/12 = 2*4^3/12 = 32 in^4
A1 = area of section 1 = b1*h1 = 4*6 = 24 in^2
A
The document contains 7 questions related to electrical circuits and concepts. The questions cover topics like calculating current given charge and time, determining energy given power and current, calculating heat dissipation in a resistor, determining motor supply current given other parameters, calculating energy cost for running a train, identifying resistor values based on color bands, and calculating lamp supply current and power for parallel circuits.
This document summarizes key concepts about transformers:
1) Transformers transfer electrical energy from one voltage level to another through magnetic coupling between primary and secondary coils. They do not directly convert electrical to mechanical energy.
2) An ideal transformer transfers power without losses, but real transformers have resistive losses in their coils and core that reduce efficiency.
3) The voltage and current ratios between primary and secondary coils are determined by their relative turn ratios; this relationship allows impedances to be transferred between sides.
- Any steady state voltage or current in a linear circuit with a sinusoidal source is a sinusoid with the same frequency as the source. Phasors and complex impedances allow conversion of differential equations to circuit analysis by representing magnitude and phase of sinusoids.
- For a resistor, the voltage and current are in phase. In the phasor domain, the resistor phasor relationship is V=IR. In the time domain, the average power dissipated is proportional to the product of RMS current and voltage.
1. The document discusses single phase AC circuits including definitions of terms like amplitude, time period, frequency, instantaneous value. It also discusses generation of sinusoidal AC voltage using a rotating coil.
2. Key concepts discussed include phasor representation, RMS and average values, form factor, phase difference, AC circuits with pure resistance and inductance. Instantaneous and average power calculations for resistive and inductive circuits are also presented.
3. Various waveforms, equations and phasor representations are used to explain these concepts for sinusoidal quantities in AC circuits.
Et201 chapter3 sinusoidal steady state circuit analysisnursheda
The document discusses sinusoidal steady state circuit analysis for purely resistive, inductive, and capacitive circuits. It defines key concepts like impedance, reactance, and phase relationships between voltage and current. Circuit analysis procedures are provided for series and parallel RLC circuits using phasor diagrams and equations. Key steps include calculating impedances and reactances, determining component voltages and currents using Ohm's law, and calculating the total current and phase angle.
This document provides an introduction to resonant circuits, discussing both series and parallel resonance. It defines resonance as occurring when the input voltage and current are in phase for a passive RLC circuit. For series resonance, the input impedance is completely real at resonance. Key equations for the resonant frequency, bandwidth, and quality factor Q are derived. Matlab programs are included to simulate the frequency response for different Q values. Duality between series and parallel circuits is also explained, where equations can be transformed between the two by substituting component values. Examples are worked through to calculate resonant components and bandwidth from given parameters.
This document summarizes the characteristics of purely resistive, inductive, and capacitive AC circuits. It also describes R-L and R-C series circuits, explaining how the current and voltage are phase shifted. Finally, it covers R-L-C series circuits in detail, showing how the phase relationship depends on whether the inductive or capacitive reactance is larger. Power calculations and definitions of impedance and power factor are provided throughout.
The document discusses sinusoidal waveforms, which are fundamental to alternating current. It defines key characteristics of sine waves such as amplitude, period, frequency, and how they are related. The document also covers how sinusoidal voltages are generated by AC generators and function generators. It describes methods for specifying the voltage value of sine waves, including peak, RMS, average and peak-to-peak values. Finally, it introduces phasors as a way to represent rotating vectors for analyzing AC circuits using trigonometry.
The document contains 7 questions related to electrical circuits and concepts. The questions cover topics like calculating current given charge and time, determining energy given power and current, calculating heat dissipation in a resistor, determining motor supply current given other parameters, calculating energy cost for running a train, identifying resistor values based on color bands, and calculating lamp supply current and power for parallel circuits.
This document summarizes key concepts about transformers:
1) Transformers transfer electrical energy from one voltage level to another through magnetic coupling between primary and secondary coils. They do not directly convert electrical to mechanical energy.
2) An ideal transformer transfers power without losses, but real transformers have resistive losses in their coils and core that reduce efficiency.
3) The voltage and current ratios between primary and secondary coils are determined by their relative turn ratios; this relationship allows impedances to be transferred between sides.
- Any steady state voltage or current in a linear circuit with a sinusoidal source is a sinusoid with the same frequency as the source. Phasors and complex impedances allow conversion of differential equations to circuit analysis by representing magnitude and phase of sinusoids.
- For a resistor, the voltage and current are in phase. In the phasor domain, the resistor phasor relationship is V=IR. In the time domain, the average power dissipated is proportional to the product of RMS current and voltage.
1. The document discusses single phase AC circuits including definitions of terms like amplitude, time period, frequency, instantaneous value. It also discusses generation of sinusoidal AC voltage using a rotating coil.
2. Key concepts discussed include phasor representation, RMS and average values, form factor, phase difference, AC circuits with pure resistance and inductance. Instantaneous and average power calculations for resistive and inductive circuits are also presented.
3. Various waveforms, equations and phasor representations are used to explain these concepts for sinusoidal quantities in AC circuits.
Et201 chapter3 sinusoidal steady state circuit analysisnursheda
The document discusses sinusoidal steady state circuit analysis for purely resistive, inductive, and capacitive circuits. It defines key concepts like impedance, reactance, and phase relationships between voltage and current. Circuit analysis procedures are provided for series and parallel RLC circuits using phasor diagrams and equations. Key steps include calculating impedances and reactances, determining component voltages and currents using Ohm's law, and calculating the total current and phase angle.
This document provides an introduction to resonant circuits, discussing both series and parallel resonance. It defines resonance as occurring when the input voltage and current are in phase for a passive RLC circuit. For series resonance, the input impedance is completely real at resonance. Key equations for the resonant frequency, bandwidth, and quality factor Q are derived. Matlab programs are included to simulate the frequency response for different Q values. Duality between series and parallel circuits is also explained, where equations can be transformed between the two by substituting component values. Examples are worked through to calculate resonant components and bandwidth from given parameters.
This document summarizes the characteristics of purely resistive, inductive, and capacitive AC circuits. It also describes R-L and R-C series circuits, explaining how the current and voltage are phase shifted. Finally, it covers R-L-C series circuits in detail, showing how the phase relationship depends on whether the inductive or capacitive reactance is larger. Power calculations and definitions of impedance and power factor are provided throughout.
The document discusses sinusoidal waveforms, which are fundamental to alternating current. It defines key characteristics of sine waves such as amplitude, period, frequency, and how they are related. The document also covers how sinusoidal voltages are generated by AC generators and function generators. It describes methods for specifying the voltage value of sine waves, including peak, RMS, average and peak-to-peak values. Finally, it introduces phasors as a way to represent rotating vectors for analyzing AC circuits using trigonometry.
This document discusses resonance in series and parallel RLC circuits. It defines key parameters for both circuit types including resonance frequency, half-power frequencies, bandwidth, and quality factor. The series resonance circuit is analyzed showing that impedance is purely resistive at resonance, with maximum current and unity power factor. Parallel resonance is also examined, with admittance being purely conductance at resonance. Formulas for calculating important resonant characteristics are provided.
The document summarizes an experiment on analyzing series and parallel RLC circuits. It describes:
1) Calculating the theoretical resonance frequency of a series RLC circuit as 18.8 kHz, but measuring it experimentally as 16.73 kHz, a difference of 11.1%.
2) Plotting the output voltage versus frequency, which reaches a minimum at the theoretical resonance point.
3) Analyzing the phase relationship and impedance characteristics at resonance, finding the voltage and current are in phase.
This document section describes alternating current (AC) circuits containing a single circuit element: resistor, inductor, or capacitor, connected to an AC voltage source. For a resistive circuit, the current and voltage are in phase. For an inductive circuit, the current lags the voltage by 90 degrees. For a capacitive circuit, the current leads the voltage by 90 degrees. The document defines important concepts such as reactance, impedance, and phasor diagrams for analyzing AC circuits.
The document discusses alternating current (AC) and direct current (DC). It defines AC as current that reverses direction periodically and describes its generation from sources like power plants. Key aspects of AC covered include its sinusoidal waveform, frequency, peak and RMS values. Phasors are introduced as a way to represent AC quantities in terms of magnitude and phase. Circuit laws for resistive AC circuits are also mentioned.
This document discusses parallel resonance in an electrical circuit. It defines parallel resonance as occurring when circuit elements are connected in parallel with their inductance and capacitance, causing impedance to rise to a maximum at the resonant frequency. The resonant frequency is where the inductive and capacitive reactances are equal. At resonance, the parallel circuit acts resistive and the impedance is at its peak while the current is at its minimum. Key characteristics of a parallel resonant circuit including impedance, current, susceptance, and bandwidth are explained.
Alternating Current -12 isc 2017 ( investigatory Project) Student
In this file, we will study about the various types of ac circuits, how they work,their phasor diagrams,types of periodic form,analytical method and graphical method to find average value of alternating current.
This document provides an overview of AC fundamentals including:
- Definitions of key terms like EMF, direct current, alternating current, sinusoid, angular velocity, frequency, time period, average value, effective value
- How electrical power is generated using alternating current
- Terminologies related to sinusoidal waveforms like instantaneous value, maximum value, phase difference
- Phasor representation of sinusoidal quantities using rotating vectors
- Properties of inductors and capacitors and their behavior in AC circuits
- Phasor algebra and representation of sinusoidal quantities using complex numbers
Q-Factor In Series and Parallel AC CircuitsSurbhi Yadav
The document defines Q factor as a measure of the quality of a resonant circuit, with a higher Q factor indicating a more narrow bandwidth. It gives the formula for Q factor as the ratio of power stored to power dissipated in a circuit. For series resonant circuits, Q equals the reactance divided by the resistance. For parallel resonant circuits with resistance in series with the inductor, Q is also defined as reactance over resistance. The document discusses how series and parallel resonant circuits behave at, below, and above resonance, and how Q factor relates to bandwidth and peak impedance/voltage in each type of circuit.
1) Effective current in an AC circuit is 0.707 times the maximum current. Effective voltage is 0.707 times the maximum voltage.
2) Inductive reactance is directly proportional to frequency and inductance. Capacitive reactance is inversely proportional to frequency and capacitance.
3) Impedance is the total opposition to current flow in an AC circuit consisting of resistance and reactance. Power is consumed only by the resistive component of impedance and is proportional to the cosine of the phase angle.
The Parallel RLC Circuit is the exact opposite to the series circuit we looked at in the previous tutorial although some of the previous concepts and equations still apply.
This document discusses fundamentals of alternating current (AC), including:
- AC voltage is generated as sinusoidal waves by power plants and used worldwide.
- Key definitions for AC waves include waveform, instantaneous value, peak amplitude, peak-to-peak value, cycle, period, and frequency.
- The basic mathematical form for a sinusoidal AC waveform is y = A sin(ωt), where A is the amplitude and ωt represents angular displacement over time.
- Root mean square (RMS) value represents the effective or heating value of AC and is calculated as the square root of the mean of the squares of the instantaneous values over one cycle.
- Average value of a symmetrical AC waveform is
- AC circuits use alternating current that constantly changes in amplitude and direction. This allows the magnitude to be easily changed using transformers.
- The sine wave is the most common AC waveform, defined by amplitude, frequency, phase, and time. Peak, RMS, and average amplitudes are important measurements.
- Impedance combines resistance with reactance from inductors and capacitors. Reactance depends on frequency and causes current to lead or lag voltage in circuits.
This document discusses sinusoidal waves and AC voltages. It defines key characteristics of sine waves like period, frequency, amplitude, and phase angle. It explains that period is the time for one full cycle and frequency is the number of cycles per second. Amplitude refers to the maximum voltage swing and is usually expressed as peak or RMS values. Phase angle represents the shift between two signals with the same frequency, with lagging signals reaching zero later than the reference.
Rc and rl differentiator and integrator circuittaranjeet10
This document describes RC and RL integrator and differentiator circuits. It provides examples of how the capacitor and inductor voltages change in response to input pulses based on the time constant. Integrator circuits sum the input to produce an output voltage, while differentiator circuits produce an output proportional to the rate of change of the input. The time constant determines whether the output follows or averages the input pulses. An application of integrators is to generate time delays.
The Parallel RLC Circuit is the exact opposite to the series circuit we looked at in the previous tutorial although some of the previous concepts and equations still apply.
Okay, let's think through this step-by-step:
* When just the resistor is connected, power is 1.000 W
* When the capacitor is added, power is 0.500 W
* When the inductor is added (without the capacitor), power is 0.250 W
* Power delivered is proportional to the square of the current. As impedance increases, current decreases.
* With just the resistor, impedance is lowest so current is highest and power is 1.000 W
* Adding the capacitor increases impedance, so current decreases and power is 0.500 W
* Adding the inductor further increases impedance, so current decreases more and power is 0.250 W
This chapter describes RC circuits and their behavior when a sinusoidal voltage is applied. Key points include: the current in an RC circuit leads the source voltage; resistor voltage is in phase with current while capacitor voltage lags current by 90 degrees; impedance of a series RC circuit decreases with increasing frequency while the phase angle decreases; and RC circuits can be used as phase shifters or filters.
This document discusses reactance in series and parallel circuits. It explains how vectors can be used to represent voltages and currents in reactive circuits, accounting for phase differences. Key concepts covered include reactance, impedance, power dissipation, and resonance, which occurs when a circuit's inductive and capacitive reactance are balanced. Figures and diagrams are provided to illustrate these electrical concepts.
This chapter discusses sinusoidal waveforms which are fundamental to alternating current (AC) circuits. Sine waves are characterized by their amplitude and period. The chapter covers definitions of peak, RMS, average values and how to relate period and frequency. It also discusses how sinusoidal voltages are generated and defines concepts like phase shift and phasors which allow analysis of AC circuits using trigonometry. The chapter concludes with an overview of pulse waveforms.
Here are the solutions to the simple harmonic motion problems:
1. Amplitude = 20 cm
Frequency = 31.4 rad/s
Period = 2π/31.4 = 0.2 s
2. Maximum displacement = 50 cm
Maximum velocity = 1000 cm/s (20π rad/s)
Maximum acceleration = 40000 cm/s^2 (400π^2 rad^2/s^2)
Number of oscillations in 5 s = 5 * 20π = 100
3. Displacement x(t) = 20 cos(2πt/0.5) cm
Velocity v(t) = -40π sin(2πt/0.5) cm
1) Uniform acceleration, energy transfer, and oscillating mechanical systems are examined in Chapter 2 on dynamic engineering systems.
2) Outcomes for Chapter 2 include analyzing dynamic systems involving uniform acceleration and determining the behavior of oscillating mechanical systems.
3) Mechanics involves the study of kinematics (motion), kinetics (forces), and statics (equilibrium) to describe the behavior of objects.
This chapter discusses dynamic engineering systems including uniform acceleration, energy transfer through various forms like potential and kinetic energy, and oscillating mechanical systems. It covers concepts like Newton's laws of motion, conservation of energy, and how energy is transferred and stored in linear and rotating systems, as well as damped oscillatory motion. Simple harmonic motion of linear and transverse systems is also qualitatively examined.
This document discusses resonance in series and parallel RLC circuits. It defines key parameters for both circuit types including resonance frequency, half-power frequencies, bandwidth, and quality factor. The series resonance circuit is analyzed showing that impedance is purely resistive at resonance, with maximum current and unity power factor. Parallel resonance is also examined, with admittance being purely conductance at resonance. Formulas for calculating important resonant characteristics are provided.
The document summarizes an experiment on analyzing series and parallel RLC circuits. It describes:
1) Calculating the theoretical resonance frequency of a series RLC circuit as 18.8 kHz, but measuring it experimentally as 16.73 kHz, a difference of 11.1%.
2) Plotting the output voltage versus frequency, which reaches a minimum at the theoretical resonance point.
3) Analyzing the phase relationship and impedance characteristics at resonance, finding the voltage and current are in phase.
This document section describes alternating current (AC) circuits containing a single circuit element: resistor, inductor, or capacitor, connected to an AC voltage source. For a resistive circuit, the current and voltage are in phase. For an inductive circuit, the current lags the voltage by 90 degrees. For a capacitive circuit, the current leads the voltage by 90 degrees. The document defines important concepts such as reactance, impedance, and phasor diagrams for analyzing AC circuits.
The document discusses alternating current (AC) and direct current (DC). It defines AC as current that reverses direction periodically and describes its generation from sources like power plants. Key aspects of AC covered include its sinusoidal waveform, frequency, peak and RMS values. Phasors are introduced as a way to represent AC quantities in terms of magnitude and phase. Circuit laws for resistive AC circuits are also mentioned.
This document discusses parallel resonance in an electrical circuit. It defines parallel resonance as occurring when circuit elements are connected in parallel with their inductance and capacitance, causing impedance to rise to a maximum at the resonant frequency. The resonant frequency is where the inductive and capacitive reactances are equal. At resonance, the parallel circuit acts resistive and the impedance is at its peak while the current is at its minimum. Key characteristics of a parallel resonant circuit including impedance, current, susceptance, and bandwidth are explained.
Alternating Current -12 isc 2017 ( investigatory Project) Student
In this file, we will study about the various types of ac circuits, how they work,their phasor diagrams,types of periodic form,analytical method and graphical method to find average value of alternating current.
This document provides an overview of AC fundamentals including:
- Definitions of key terms like EMF, direct current, alternating current, sinusoid, angular velocity, frequency, time period, average value, effective value
- How electrical power is generated using alternating current
- Terminologies related to sinusoidal waveforms like instantaneous value, maximum value, phase difference
- Phasor representation of sinusoidal quantities using rotating vectors
- Properties of inductors and capacitors and their behavior in AC circuits
- Phasor algebra and representation of sinusoidal quantities using complex numbers
Q-Factor In Series and Parallel AC CircuitsSurbhi Yadav
The document defines Q factor as a measure of the quality of a resonant circuit, with a higher Q factor indicating a more narrow bandwidth. It gives the formula for Q factor as the ratio of power stored to power dissipated in a circuit. For series resonant circuits, Q equals the reactance divided by the resistance. For parallel resonant circuits with resistance in series with the inductor, Q is also defined as reactance over resistance. The document discusses how series and parallel resonant circuits behave at, below, and above resonance, and how Q factor relates to bandwidth and peak impedance/voltage in each type of circuit.
1) Effective current in an AC circuit is 0.707 times the maximum current. Effective voltage is 0.707 times the maximum voltage.
2) Inductive reactance is directly proportional to frequency and inductance. Capacitive reactance is inversely proportional to frequency and capacitance.
3) Impedance is the total opposition to current flow in an AC circuit consisting of resistance and reactance. Power is consumed only by the resistive component of impedance and is proportional to the cosine of the phase angle.
The Parallel RLC Circuit is the exact opposite to the series circuit we looked at in the previous tutorial although some of the previous concepts and equations still apply.
This document discusses fundamentals of alternating current (AC), including:
- AC voltage is generated as sinusoidal waves by power plants and used worldwide.
- Key definitions for AC waves include waveform, instantaneous value, peak amplitude, peak-to-peak value, cycle, period, and frequency.
- The basic mathematical form for a sinusoidal AC waveform is y = A sin(ωt), where A is the amplitude and ωt represents angular displacement over time.
- Root mean square (RMS) value represents the effective or heating value of AC and is calculated as the square root of the mean of the squares of the instantaneous values over one cycle.
- Average value of a symmetrical AC waveform is
- AC circuits use alternating current that constantly changes in amplitude and direction. This allows the magnitude to be easily changed using transformers.
- The sine wave is the most common AC waveform, defined by amplitude, frequency, phase, and time. Peak, RMS, and average amplitudes are important measurements.
- Impedance combines resistance with reactance from inductors and capacitors. Reactance depends on frequency and causes current to lead or lag voltage in circuits.
This document discusses sinusoidal waves and AC voltages. It defines key characteristics of sine waves like period, frequency, amplitude, and phase angle. It explains that period is the time for one full cycle and frequency is the number of cycles per second. Amplitude refers to the maximum voltage swing and is usually expressed as peak or RMS values. Phase angle represents the shift between two signals with the same frequency, with lagging signals reaching zero later than the reference.
Rc and rl differentiator and integrator circuittaranjeet10
This document describes RC and RL integrator and differentiator circuits. It provides examples of how the capacitor and inductor voltages change in response to input pulses based on the time constant. Integrator circuits sum the input to produce an output voltage, while differentiator circuits produce an output proportional to the rate of change of the input. The time constant determines whether the output follows or averages the input pulses. An application of integrators is to generate time delays.
The Parallel RLC Circuit is the exact opposite to the series circuit we looked at in the previous tutorial although some of the previous concepts and equations still apply.
Okay, let's think through this step-by-step:
* When just the resistor is connected, power is 1.000 W
* When the capacitor is added, power is 0.500 W
* When the inductor is added (without the capacitor), power is 0.250 W
* Power delivered is proportional to the square of the current. As impedance increases, current decreases.
* With just the resistor, impedance is lowest so current is highest and power is 1.000 W
* Adding the capacitor increases impedance, so current decreases and power is 0.500 W
* Adding the inductor further increases impedance, so current decreases more and power is 0.250 W
This chapter describes RC circuits and their behavior when a sinusoidal voltage is applied. Key points include: the current in an RC circuit leads the source voltage; resistor voltage is in phase with current while capacitor voltage lags current by 90 degrees; impedance of a series RC circuit decreases with increasing frequency while the phase angle decreases; and RC circuits can be used as phase shifters or filters.
This document discusses reactance in series and parallel circuits. It explains how vectors can be used to represent voltages and currents in reactive circuits, accounting for phase differences. Key concepts covered include reactance, impedance, power dissipation, and resonance, which occurs when a circuit's inductive and capacitive reactance are balanced. Figures and diagrams are provided to illustrate these electrical concepts.
This chapter discusses sinusoidal waveforms which are fundamental to alternating current (AC) circuits. Sine waves are characterized by their amplitude and period. The chapter covers definitions of peak, RMS, average values and how to relate period and frequency. It also discusses how sinusoidal voltages are generated and defines concepts like phase shift and phasors which allow analysis of AC circuits using trigonometry. The chapter concludes with an overview of pulse waveforms.
Here are the solutions to the simple harmonic motion problems:
1. Amplitude = 20 cm
Frequency = 31.4 rad/s
Period = 2π/31.4 = 0.2 s
2. Maximum displacement = 50 cm
Maximum velocity = 1000 cm/s (20π rad/s)
Maximum acceleration = 40000 cm/s^2 (400π^2 rad^2/s^2)
Number of oscillations in 5 s = 5 * 20π = 100
3. Displacement x(t) = 20 cos(2πt/0.5) cm
Velocity v(t) = -40π sin(2πt/0.5) cm
1) Uniform acceleration, energy transfer, and oscillating mechanical systems are examined in Chapter 2 on dynamic engineering systems.
2) Outcomes for Chapter 2 include analyzing dynamic systems involving uniform acceleration and determining the behavior of oscillating mechanical systems.
3) Mechanics involves the study of kinematics (motion), kinetics (forces), and statics (equilibrium) to describe the behavior of objects.
This chapter discusses dynamic engineering systems including uniform acceleration, energy transfer through various forms like potential and kinetic energy, and oscillating mechanical systems. It covers concepts like Newton's laws of motion, conservation of energy, and how energy is transferred and stored in linear and rotating systems, as well as damped oscillatory motion. Simple harmonic motion of linear and transverse systems is also qualitatively examined.
The aim of this unit is to investigate a number of major scientific principles that underpin the design and operation of engineering systems. It is a broad-based unit, covering both mechanical and electrical principles. It is intended to give an overview that will provide the basis for further study in specialist areas of engineering.
This document summarizes key concepts related to static engineering systems including:
- Types of columns that can fail in true compression (short columns) or buckle before reaching full strength (long columns).
- Types of beams classified by their support conditions.
- Loads that can be applied to beams as concentrated loads or uniformly distributed loads.
- Shear forces and bending moments that develop in beams due to applied loads, and sign conventions for positive and negative shear forces and moments.
- Relationships for calculating shear forces and bending moments along beams subjected to different load types.
- Examples of determining shear forces and bending moments at points along cantilever beams and beams with various concentrated and uniform loads
Here are the key points about momentum and impulse:
- Momentum is the product of an object's mass and velocity. It represents the amount of motion an object has.
- Impulse is the product of force and the time over which it acts. It represents the change in an object's momentum due to a force.
- Impulse and change in momentum are directly related - a large impulse (large force or long duration) results in a large change in momentum.
- Both momentum and impulse are vector quantities, having both magnitude and direction associated with the motion or force.
So in summary, momentum describes the amount of motion, while impulse describes the force applied to change an object's motion and momentum.
This document discusses static engineering systems and structural members experiencing bending. It covers key concepts such as:
- The bending of structural members and the neutral axis where the length remains unchanged during bending.
- How bending stress varies across a beam's cross-section, with maximum stress occurring on the surfaces furthest from the neutral axis.
- The general bending formula that relates bending moment, stress, elastic modulus, and distance from the neutral axis.
- Other bending concepts like the second moment of area, parallel axis theorem, and position of the neutral axis through the centroid.
Worked examples demonstrate calculating bending stresses, moments, strains, and selecting suitable beam dimensions.
1) Motion can be described relative to a reference point, such as describing a car's motion relative to the road surface.
2) Speed is the distance an object covers over a set period of time. It does not include direction. Velocity includes both speed and direction.
3) Acceleration is the rate of change of an object's velocity. It can be positive (speeding up) or negative (slowing down). Changing direction at a constant speed is also considered acceleration.
The document discusses various characteristics of materials including:
1. Density, which is the relationship between mass and volume of a material. Materials like cork have lower density than lead.
2. Hygroscopic materials, which absorb water, like cellulose and silica gel. Less hygroscopic materials are used to make waterproof tests.
3. Thermal conductivity, with metals being good conductors and plastics, ceramics, wood, and cork being good insulators.
The document discusses torsion in circular shafts. It covers the assumptions in torsion theory including the determination of shear stress, strain, and modulus. It also describes the distribution of shear stress and angle of twist in solid and hollow circular shafts. Key points include:
- Shear stress is highest at the surface and decreases linearly towards the center of a shaft.
- Angle of twist is proportional to both the applied torque and length of the shaft.
- Cross sections remain plane during twisting for circular shafts but may become distorted for non-circular shafts.
This document provides an overview of advanced power system protection topics including definitions, objectives of power system protection, relay characteristics, methods of discrimination, distance protection, current balance protection, phase comparison protection, fault detection techniques using zero sequence systems, sequence filters, general relay equations, fuses, and time-current characteristics. It discusses concepts such as discrimination, stability, sensitivity, repeatability and provides examples to illustrate relay equations and characteristics.
The document discusses Auger electron emission and Auger electron spectroscopy. It describes how Auger electrons are emitted when an atom relaxes from an excited state following ionization. It also discusses how AES can be used to identify elements based on peak positions and obtain quantitative composition by comparing peak intensities to sensitivity factors. The technique provides chemical information through variations in peak shape and can determine properties like thickness and growth mode of thin films.
The document summarizes different types of AC bridges used to measure inductance (L) and capacitance (C) values. It describes Maxwell, Hay, Schering, and Wien bridges. The Maxwell bridge measures inductors with low Q values by balancing reactance and resistance. The Hay bridge measures high Q inductors using two equations solved simultaneously. The Schering bridge directly provides Cx and Rx values from balancing equations. The Wien bridge determines an unknown frequency by balancing the bridge at that frequency.
This document presents a dynamic model of a permanent magnet synchronous motor using a two-phase d-q model. It derives the two-phase model equations from the three-phase model equations. It discusses how the inductances and flux linkages vary with rotor position and defines the d-axis and q-axis components. It presents the two-phase equivalent circuit model and discusses how torque is produced from both the permanent magnet flux and reluctance torque. It also discusses how to obtain the two-phase model parameters from physical measurements of the motor.
This document presents a dynamic model of a permanent magnet synchronous motor. It derives a two-phase d-q model from the three-phase model by transforming the stator variables from the stationary a-b-c frame to the rotating d-q frame. It discusses obtaining the complete set of model parameters from simple laboratory tests, as some parameters are not directly measurable and vary with operating conditions. The model is primarily for interior permanent magnet synchronous motors but can also apply to surface permanent magnet motors.
Torsional vibrations and buckling of thin WALLED BEAMSSRINIVASULU N V
The document discusses the torsional vibrations and buckling of thin-walled beams on elastic foundation using a dynamic stiffness matrix method. It develops analytical equations to model the behavior of clamped-simply supported beams under an axial load and resting on an elastic foundation. Numerical results are presented for natural frequencies and buckling loads for different values of warping and foundation parameters. The dynamic stiffness matrix approach can accurately analyze beams with non-uniform cross-sections and complex boundary conditions.
The document summarizes research analyzing 3D stress intensity factors (SIF) for arrays of inner radial lunular or crescentic cracks in thin and thick-walled spherical pressure vessels. Finite element analysis was used to evaluate SIF distributions along crack fronts for various crack configurations, sphere geometries, crack depths, and ellipticities. The results provide insight into how SIF is affected by these parameters to better predict fatigue life and fracture of spherical pressure vessels.
This document summarizes key concepts about columns and struts. It defines struts as structural members under axial compression, while columns are vertical struts. Columns can be short or long depending on their length-to-minimum radius of gyration ratio. Euler's formula and Rankine's formula provide methods to calculate the buckling/crippling load of columns based on factors like the modulus of elasticity, moment of inertia, and effective length. The document also discusses radius of gyration, slenderness ratio, crushing load, and how eccentric loading affects column stresses.
The document provides definitions and explanations of key concepts in quantum mechanics and atomic structure, including:
- The formula for the energy of a photon
- Definitions of wave function, probability density, electron density, orbitals, electron shells, subshells, degeneracy, Pauli exclusion principle, electron configuration, and Hund's rule
- Tables listing the allowed values of the principal, angular momentum, magnetic, and spin quantum numbers
- Examples of specifying orbitals using n, l, and ml values
- Examples of writing electron configurations in both long and short hand notation for various elements
Crystal structure determination uses X-ray diffraction to analyze the arrangement of atoms in crystals. X-rays are diffracted by the periodic lattice of a crystal in predictable ways. Bragg's law describes the conditions under which constructive interference occurs between X-rays reflected from different crystal lattice planes, producing intense diffracted beams. By measuring the angles and intensities of these diffracted beams, researchers can determine the size and shape of the unit cell and deduce the positions of atoms within the cell. The reciprocal lattice formalism relates diffraction phenomena to the periodicity of the crystal lattice.
Uniten iccbt 08 a serviceability approach to the design of scc beamsYf Chong
This document proposes a method to determine the span to effective depth ratio of self-compacting concrete (SCC) beams based on deflection limits. It uses an effective moment of inertia function to calculate short-term and long-term deflections, which are then set equal to the permissible deflection of span/250. This results in an equation to calculate the limiting span to effective depth ratio. Design charts are presented showing the ratio varies based on steel ratio and the ratio of sustained to service load. The method was developed using a simplified effective moment of inertia equation. It was verified against test data and can provide guidance for the design of SCC beams.
This document provides an introduction to elastic-plastic fracture mechanics (EPFM). It discusses the key concepts of EPFM including crack tip opening displacement (CTOD) and the J-integral. CTOD and J-integral are used to characterize fracture toughness in large-scale plastic deformation, unlike linear elastic fracture mechanics (LEFM) which is only valid for small plastic zones. Measurement methods and applications of CTOD and J-integral are also covered along with background on plasticity theory and LEFM concepts.
R,L,C, G parameters of a co-axial & 2-wire transmission line
Field solutions for TE and TM modes for a waveguide
Design and analysis of rectangular waveguide to support TE10 mode
Design and analysis of circular waveguide to support TE11 mode
This document contains the teaching schedule and lecture topics for a course on complex strains taught by Dr. Alessandro Palmeri. The course covers various topics related to complex stress and strain analysis, including beam shear stresses, shear centres, virtual forces, compatibility methods, moment distribution methods, column stability, unsymmetric bending, and complex stress/strain analysis. Lectures are delivered by Dr. Palmeri and other staff members. Tutorial sessions are also included to provide examples and applications of the taught concepts. The schedule lists the topics to be covered in each week across the 12-week term, with exams occurring in the final two weeks.
Waveguiding Structures Part 2 (Attenuation).pptxPawanKumar391848
1. The document discusses attenuation in waveguiding structures due to dielectric loss and conductor loss. It provides expressions for calculating the attenuation constant for these two loss mechanisms.
2. It defines the surface resistance of a conductor and derives an expression for it based on the material conductivity and frequency. The surface resistance is related to an effective surface current density.
3. Approximations are made to calculate the dielectric attenuation constant for the TEM mode and general waveguide modes based on assuming small dielectric losses. Expressions for the attenuation constants are provided.
This document summarizes a multiphysics simulation of a packed bed reactor. It presents the reactor geometry, kinetic reaction models, and approaches taken for both lumped and heterogeneous models. Results shown include temperature distributions, average temperature and conversion profiles along the reactor length, as well as conversions for specific segments. The conclusion suggests further modeling to study hot spots near the inlet and potential intra-pellet heat transfer effects.
The document describes the design of a bungee jumping system using rubber bands, including calculating the spring constant of individual rubber bands and determining that a chain of 1.2 rubber bands would be required based on conservation of energy calculations. It also analyzes the period of oscillation and time for the system to settle in water after being dropped, finding values that align with experimental results.
A comparison of VLSI interconnect modelshappybhatia
This document presents a comparative study of delay analysis for carbon nanotube and copper based VLSI interconnect models. It outlines the introduction, interconnect models, factors affecting interconnect performance, and comparison of CNT vs copper. It then discusses analytical delay estimation using the driver interconnect model and modified nodal analysis, as well as SPICE simulation results comparing CNT and copper. The goal is to analyze and compare the delay performance of CNT and copper interconnects.
The document describes information and energy control systems. It discusses block diagrams of typical information systems like audio and process monitoring systems. It explains how electrical signals convey system information and the functions of system components like transducers, amplifiers, oscillators, analog to digital converters and digital to analog converters. It also discusses the effects of noise on systems and how system output is determined from a given input.
This document summarizes key concepts about transformers:
1) Transformers transfer electrical energy from one voltage level to another through a magnetic field without changing frequency. They have a primary and secondary winding wound around an iron core.
2) An AC voltage applied to the primary induces a voltage in the secondary according to Faraday's Law of induction. The ratio of voltages is determined by the ratio of turns in the windings.
3) Real transformers have losses that are modeled in an equivalent circuit including resistances of the windings and core and a magnetizing reactance. Impedances can be transferred between windings using the turns ratio.
This document discusses DC and AC theory, including:
1) Key DC electrical principles such as Ohm's and Kirchhoff's laws, voltage and current dividers, and fundamental relationships involving resistance, inductance, capacitance.
2) Definitions of electrical current, voltage, resistors, and an introduction to Ohm's law.
3) The differences between direct current (DC) and alternating current (AC) and examples of their waveforms. Kirchhoff's laws and their use in circuit analysis are also covered.
The magnetic field produced by an electric current has
direction, strength and geometry that depends on:
1. The direction of the current. The magnetic field circulates around the wire.
2. The amount of current. The stronger the current, the stronger the magnetic field.
3. The distance from the wire. The magnetic field strength decreases with distance from the wire.
So in summary, an electric current flowing through a wire produces a magnetic field that encircles the wire, with a strength that decreases with distance from the wire and depends on the amount of current. The direction of the magnetic field is given by the right-hand rule.
This document discusses the selection and design of standard steel beams and columns. It provides information on:
1) How to select standard steel sections from reference tables that list section properties like elastic section modulus.
2) How to calculate required section modulus based on maximum bending moment and allowable stress.
3) Guidelines for selecting sections, including choosing sections that minimize weight for beams and have slenderness ratios below 180 for columns.
4) An example of designing a simply supported beam by calculating bending moment, allowable stress, and required section modulus.
The document discusses the design of ventilation, air conditioning, and other building systems. It outlines the purpose of ventilation systems to provide occupant comfort while saving energy. Important factors to consider for ventilation design include the local climate, building air tightness, and pressure balances. When selecting an air conditioning system, factors like room size, windows, occupants, and heat sources must be evaluated. Fire protection requirements include posting the fire safety plan at entrances and distributing copies to tenants.
This document discusses static engineering systems and specifically simply supported beams. It covers topics such as determination of shear force, bending moment, stress due to bending, eccentric loading of columns, stress distribution, and the middle third rule. It also defines short and long columns, different types of beam supports, and how loads can be applied to beams as concentrated or distributed loads. The document discusses shear forces and bending moments created by loads on beams and provides conventions for defining positive and negative shear forces and bending moments. It also provides relationships and diagrams for shear forces and bending moments under different load conditions including concentrated loads, uniform loads, and multiple concentrated loads. An example problem is also included.
Here are the steps to solve this example:
1) Find the moment of inertia, I, of the composite section about the neutral axis:
I = I1 + I2 + A1*d1^2 + A2*d2^2
Where:
I1 = moment of inertia of rectangular section 1 = b1*h1^3/12 = 4*6^3/12 = 144 in^4
I2 = moment of inertia of rectangular section 2 = b2*h2^3/12 = 2*4^3/12 = 32 in^4
A1 = area of section 1 = b1*h1 = 4*6 = 24 in^2
A
हिंदी वर्णमाला पीपीटी, hindi alphabet PPT presentation, hindi varnamala PPT, Hindi Varnamala pdf, हिंदी स्वर, हिंदी व्यंजन, sikhiye hindi varnmala, dr. mulla adam ali, hindi language and literature, hindi alphabet with drawing, hindi alphabet pdf, hindi varnamala for childrens, hindi language, hindi varnamala practice for kids, https://www.drmullaadamali.com
How to Setup Warehouse & Location in Odoo 17 InventoryCeline George
In this slide, we'll explore how to set up warehouses and locations in Odoo 17 Inventory. This will help us manage our stock effectively, track inventory levels, and streamline warehouse operations.
Leveraging Generative AI to Drive Nonprofit InnovationTechSoup
In this webinar, participants learned how to utilize Generative AI to streamline operations and elevate member engagement. Amazon Web Service experts provided a customer specific use cases and dived into low/no-code tools that are quick and easy to deploy through Amazon Web Service (AWS.)
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
Temple of Asclepius in Thrace. Excavation resultsKrassimira Luka
The temple and the sanctuary around were dedicated to Asklepios Zmidrenus. This name has been known since 1875 when an inscription dedicated to him was discovered in Rome. The inscription is dated in 227 AD and was left by soldiers originating from the city of Philippopolis (modern Plovdiv).
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) CurriculumMJDuyan
(𝐓𝐋𝐄 𝟏𝟎𝟎) (𝐋𝐞𝐬𝐬𝐨𝐧 𝟏)-𝐏𝐫𝐞𝐥𝐢𝐦𝐬
𝐃𝐢𝐬𝐜𝐮𝐬𝐬 𝐭𝐡𝐞 𝐄𝐏𝐏 𝐂𝐮𝐫𝐫𝐢𝐜𝐮𝐥𝐮𝐦 𝐢𝐧 𝐭𝐡𝐞 𝐏𝐡𝐢𝐥𝐢𝐩𝐩𝐢𝐧𝐞𝐬:
- Understand the goals and objectives of the Edukasyong Pantahanan at Pangkabuhayan (EPP) curriculum, recognizing its importance in fostering practical life skills and values among students. Students will also be able to identify the key components and subjects covered, such as agriculture, home economics, industrial arts, and information and communication technology.
𝐄𝐱𝐩𝐥𝐚𝐢𝐧 𝐭𝐡𝐞 𝐍𝐚𝐭𝐮𝐫𝐞 𝐚𝐧𝐝 𝐒𝐜𝐨𝐩𝐞 𝐨𝐟 𝐚𝐧 𝐄𝐧𝐭𝐫𝐞𝐩𝐫𝐞𝐧𝐞𝐮𝐫:
-Define entrepreneurship, distinguishing it from general business activities by emphasizing its focus on innovation, risk-taking, and value creation. Students will describe the characteristics and traits of successful entrepreneurs, including their roles and responsibilities, and discuss the broader economic and social impacts of entrepreneurial activities on both local and global scales.
Bed Making ( Introduction, Purpose, Types, Articles, Scientific principles, N...
Engineering science lesson 5
1. Chapter 1- Static engineering systems
1.1 Simply supported beams
1.1.1 determination of shear force
1.1.2 bending moment and stress due to bending
1.1.3 radius of curvature in simply supported beams subjected to
concentrated and uniformly distributed loads
1.1.4 eccentric loading of columns
1.1.5 stress distribution
1.1.6 middle third rule
1.2 Beams and columns
1.2.1 elastic section modulus for beams
1.2.2 standard section tables for rolled steel beams
1.2.3 selection of standard sections (eg slenderness ratio for
compression members, standard section and allowable
stress tables for rolled steel columns, selection of standard
sections)
1
2. Stresses in beams
• Stresses in the beam are functions of x and y
• If we were to cut a beam at a point x, we would find a distribution of
direct stresses σ(y) and shear stresses σxy(y)
• Summing these individual moments over the area of the cross-section is
the definition of the moment resultant M,
• Summing the shear stresses on the cross-section is the definition of the
shear resultant V,
• The sum of all direct stresses acting on the cross-section is known as N,
2
3. • Direct stress distribution in the beam due to bending
• Note that the bending stress in beam theory is linear
through the beam thickness. The maximum bending
stress occurs at the point furthest away from the neutral
axis, y = c
3
4. Flexure formula
•
Stresses calculated from the flexure formula are called bending
stresses or flexural stresses.
• The maximum tensile and compressive bending stresses occur at
points (c1 and c2) furthest from the neutral surface
• where S1 and S2 are called section moduli (units: in3, m3) of the cross-
sectional area. Section moduli are commonly listed in design
4
handbooks
9. Design of columns under centric loads
• Experimental data demonstrate
- for large Le/k σcr follows
le /r,
(le/k)2 Euler’s formula and depends
upon E but not σY.
- for small L/k σcr is
le e/r,
determined by the yield
strength σY and not E.
- for intermediate Le/k σcr
le /r,
depends on both σY and E.
9
10. • For Le/r > Cc
l e/k
Structural Steel
π 2E σ
σ cr = σ all = cr
American Inst. of Steel Construction ( Le/kr ) 2 FS
l /
FS = 1.92
l e/k
• For Le/r > Cc
( Le /kr ) 2
le / σ
σ cr = σ Y 1 − 2
σ all = cr
2Cc FS
3
5 3 Le/kr 1 Le/k
l / l /r
FS = + e − e
3 8 Cc 8 Cc
le/k • At Le/k = Cc
le /r
2
2 2π E
σ cr = 1 σ Y Cc =
2 σY
10
11. Sample problem
SOLUTION:
• With the diameter unknown, the
slenderness ration can not be evaluated.
Must make an assumption on which
slenderness ratio regime to utilize.
• Calculate required diameter for
assumed slenderness ratio regime.
• Evaluate slenderness ratio and verify
initial assumption. Repeat if
Using the aluminum alloy2014-T6, necessary.
determine the smallest diameter rod
which can be used to support the centric
load P = 60 kN if a) L = 750 mm,
b) L = 300 mm
11
12. • For L = 750 mm, assume L/r > 55
• Determine cylinder radius:
P 372 × 103 MPa
σ all = =
A ( L r)2
60 × 103 N 372 × 103 MPa
2
= 2
c = 18.44 mm
πc 0.750 m
c/2
• Check slenderness ratio assumption:
c = cylinder radius
L L 750mm
r = radius of gyration = = = 81.3 > 55
r c / 2 (18.44 mm )
I πc 4 4 c assumption was correct
= = 2
=
A πc 2
d = 2c = 36.9 mm
12
13. • For L = 300 mm, assume L/r < 55
• Determine cylinder radius:
P L
σ all = = 212 − 1.585 MPa
A r
60 × 103 N 0.3 m 6
= 212 − 1.585 × 10 Pa
πc 2 c / 2
c = 12.00 mm
• Check slenderness ratio assumption:
L L 300 mm
= = = 50 < 55
r c / 2 (12.00 mm )
assumption was correct
d = 2c = 24.0 mm
13
14. Eccentric loading of columns
• Generally, columns are designed so
that the axial load is inline with the
column
• There are situations that the load will
be off center and cause a bending in
the column in addition to the
Pin-Pin Column
compression. This type of loading is
called eccentric load with Eccentric
Axial Load
• When a column is load off center,
bending can be sever problem and
may be more important than the
compression stress or buckling 14
15. Analysis of eccentric loads
• At the cut surface, there will be both an internal
moment, m, and the axial load P. This partial
section of the column must still be equilibrium,
and moments can be summed at the cut
surface, giving,
ΣM = 0
m + P (e + v) = 0
• bending in a structure can be modeled as m =
EI d2v/dx2, giving
EI d2v/dx2 + Pv = -Pe
• This is a classical differential equation that can
be solved using the general solution,
v = C2 sin kx + C1 cos kx - e
where k = (P/EI)0.5. The constants C1 and C2 can
be determined using the boundary conditions 15
16. • First, the deflection, v=0, at x = 0
0 = C2 0 + C1 1 - e
C1 = e
• The second boundary condition specifies the deflection, v=0, at X = L
0 = C2 sin kL + e cos kL - e
C2=e tan (kL/2)
• Maximum deflection
– The maximum deflection occurs at the column center, x = L/2, since both
ends are pinned.
16
17. Maximum stress: secant formula
• Unlike basic column buckling, eccentric
loaded columns bend and must
withstand both bending stresses and
axial compression stresses.
• The axial load P, will produce a
compression stress P/A. Since the load
P is not at the center, it will cause a
bending stress My/I.
• The maximum moment, Mmax, is at
the mid-point of the column (x = L/2),
Mmax = P (e + vmax)
17
18. • Combining the above equations gives
• But I = Ar2. This gives the final form of the secant formula as
• The stress maximum, σmax, is generally the yield stress or
allowable stress of the column material, which is known.
• The geometry of the column, length L, area A, radius of
gyration r, and maximum distance from the neutral axis c
are also known. The eccentricity, e, and material stiffness,
E, are considered known.
18
20. Design of columns under an eccentric load
• An eccentric load P can be replaced by a
centric load P and a couple M = Pe.
• Normal stresses can be found from
superposing the stresses due to the
centric load and couple,
σ = σ centric + σ bending
P Mc
σ max = +
A I
• Allowable stress method:
P Mc
+ ≤ σ all
A I
• Interaction method:
P A Mc I
+ ≤1
( σ all ) centric ( σ all ) bending
20
21. Example
The uniform column consists of an 8-ft section
of structural tubing having the cross-section
shown.
a) Using Euler’s formula and a factor of safety
of two, determine the allowable centric load
for the column and the corresponding
normal stress.
b) Assuming that the allowable load, found in
part a, is applied at a point 0.75 in. from the
geometric axis of the column, determine the
horizontal deflection of the top of the
column and the maximum normal stress in
the column.
21
22. SOLUTION:
• Maximum allowable centric load:
- Effective length,
Le = 2( 8 ft ) = 16 ft = 192 in.
- Critical load,
Pcr =
π 2 EI
=
( )(
π 2 29 × 106 psi 8.0 in 4 )
2
Le (192 in ) 2
= 62.1 kips
- Allowable load,
P 62.1 kips Pall = 31.1 kips
Pall = cr =
FS 2
P 31.1 kips
σ = all = σ = 8.79 ksi
A 3.54 in 2 22
23. • Eccentric load:
- End deflection,
π P
ym = e sec
2 P − 1
cr
π
= ( 0.075 in ) sec − 1
2 2
ym = 0.939 in.
- Maximum normal stress,
P ec π P
σm = 1 + 2 sec
2 P
A r cr
31.1 kips ( 0.75 in )( 2 in ) π
= 2
1+ sec
3.54 in (1.50 in ) 2 2 2
σ m = 22.0 ksi
23
24. Example
Determine the maximum flexural stress produced by a resisting Moment Mr of
+5000ft.lb if the beam has cross section shown in the figure.
Locate the neutral axis from the bottom end
24