answer must not be in x10 whatever but just inches as the question asks Use Castigliano's theorem to determine the magnitude of deflection at midspan for the solid steel shaft shown in the figure, where a =3 in, b = 7 in, da = 1.125 in, db = 1.875 in, and w=160 lbf/in.da7kadbWbdaa →The magnitude of deflection at the mid-span of the beam is 0.016265in.

Answered: Castigliano's theorem to determine the…

Castigliano's theorem to determine the magnitude of deflection at midspan for the solid steel b = 7 in, da = 1.125 in, db = 1.875 in, and w=160 lbf/in. da 7 d₂ W ↓ da

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter9: Deflections Of Beams

Section: Chapter Questions

Problem 9.6.10P: -10 The simple beam AB shown in the figure supports two equal concentrated loads P: one acting...

See similar textbooks

Related questions

Q: Machine Analysis The tractor boom supports the uniform mass of 500 kg in the bucket which has a…

A: Mass =500 kg weight=500×9.81 =4905 N

Q: a) How can we test which can withstandthe most stress, a length of spider web thread or a steel wire…

A: Formula used: Write the expression for the stress. σ=E×ε Here, σ is stress, E is plastic modulus and…

Q: COMBUSTION ENGINEERING (Upvote will be given. Write the complete solutions. Solve in 2 decimal…

A: For air standard dual cycle:Properties before the isentropic compression are: P1=100 kPa and…

Q: A tank contains exactly one kilogram of water consisting of liquid and vapor in equilibrium at 1…

A: Given, M = 1 kg P = 1 MPa Vf = 0.25 V Vg = 0.75 V Determine :- The enthalpy of the contents of the…

Q: Reduce the forces acting on the beam in the figure to an equivalent singular force and couple at…

Q: 12. A 200 lb force P is exerted on the lever. What will be the deformation, in inches, in the 0.0630…

A: The force applied on the right side of the lever is, P= 200 lb The length of the steel wire attached…

Q: A disk with mass m = 6.5 kg and radius R = 0.39 m hangs from a rope attached to the ceiling. The…

A: Given: m=6.5 kgR=0.39 mr=1.32 mf=18.9 rev/s

Q: One pound of air (consider here a perfect gas) with an initial temperature of 200F is allowed to…

Q: how your complete solution

A: Given Tensile stress = 65,000 psi Design stress = 9500 psi Diameter, D = 5 ft…

Q: Draw the mechanism on the side schematically, determine the parameters of the links. Draw the…

Q: Calculate the force in member BG using a freebody diagram of the rigid member ABC. The force is…

A: Given data:- To find :-The force in the member BG

Q: Ammonia enters the expansion valve of a refrigeration system at a pressure of 10 bar and a…

Q: Problem #2 Calculate the increase in stress for each segment of the compound bar shown in the figure…

Q: Bug B is crawling radially outward on the spoke of a wheel at a constant speed of 4 cm/s relative to…

A: Given: Bug's speed relative to the spoke of the wheel= 4 cm/s. Center of the wheel's velocity…

Q: Gears A and B mesh with a gear ratio n. they are fixed to circular shafts of equal length and equal…

A: Length of shafts, LA=LB=LDiameter of shafts, dA=dB=dDiameter of gear A= DADiameter of gear B=DBGear…

Q: 1. In curvilinear motion, the direction of the instantaneous acceleration is always a. tangent to…

A: The correct option. Concept used: Curvilinear motion: The curvilinear motion refers to the motion of…

Q: counterweight is 200g, goal is to shoot a 7g clay ball 3 meters. B) Find velocity vector of the…

Q: A vertical steel standpipe is 3 m in inside diameter and 30 m high. The tank is filled with water…

A: The Inside diameter of the pipe,D=3 m. Height of the tank,H=30 m. The yield strength of the…

Q: Which of the following processes is spontaneous? A) Heat coming out of an open oven. B) A puddle…

A: Spontaneous process: The process which occurs on its own without any external source required.

Q: A 3-in.-diameter horizontal water jet having a velocity of 97 ft/s strikes a curved plate, which…

A: The force required to hold the plate. Given: The diameter of the water jet is d=3 in=0.25 ft. The…

Q: Use Castigliano's theorem to determine the magnitude of deflection at midspan for the solid steel…

A: The dimensions are a=3 in, b=7 in, da=1.125 in, db=1.875 in The distributed load is w=160 lb/in

Q: If point C is the center of bar BD, why is CD measured as 24in and not sqrt(24^2 + 10^2)/2 or 24/2?…

A: We know that, motion of any link in a mechanism is general motion i.e. combination of rotation and…

Q: A piston with an outer diameter of 124.75 mm and a length of 75 mm is pushed upwards at a constant…

Q: 4. If the position of a particle is defined by = (1.5t²+1)+(4t-1)} (m), determine its speed at t = 1…

A: This question is based on the concept of kinematics and motion.

Q: I cant see the solution. It is cut off on the right side.

Q: Reduce the forces acting on the beam in the figure to an equivalent singular force and couple at…

Q: The suitability of a type K thermocouple in testing the safety of heating appliances.

A: Given data:- Thermocouple:-A thermocouple is a type of temperature sensor that detects changes in…

Q: Each pulley has a weight of 10 lb. (Figure 1) If each cord can support a maximum tension of 600…

A: The weight of pulleyWp=10 lb The maximum tension by the each cord T=600 lb

Q: The input crank link with a radius of 80 mm turns with a constant angular velocity @ = 4 rad/sec and…

A: The angular velocity of crank link is ω=4j⇀ rad/s

Q: The simple pendulum A of mass ma = 3.9 kg and length I = 1.51 m is suspended from the trolley B of…

A: Given Data: mA=3.9 kgl=1.51 mmB=7.9 kg To Find: Velocity of trolley B, vB.

Q: The assembly consisting of a uniform slender bar (mass= 1.5 kg and L=0.49 m) and a rigidly attached…

A: The initial angular acceleration. Given: The mass of the slender bar is mb=1.5 kg. The length of the…

Q: Consider laminar flow of water in a 0.9-cm-diameter pipe at a rate of 1.15 L/min. The velocity (m/s)…

A: we got d=0.009m Q=2.9167×10^-5 m^3/sec

Q: 3. A particle is traveling along the path y = 0.75x. If the position along the x axis is x = (8t) m,…

Q: 2. Two prismatic bars of a by b rectangular cross section are glued as shown in Fig. 2. The…

A: To Find:The maximum axial load (P) that can be applied without failure. Given:The limiting normal…

Q: 10 cm B 5 cm F

A: Given, d= 5mm F= 15KN RA is the net reaction force at pin A.

Q: A "swing ride" is shown in the figure. For b=1.6 m, L=3.8 m and 0=31° neglect the mass of the cables…

A: A “swing ride” is shown in the figure, b=1.6m L=3.8m θ=31°, mass (m)=33kg To find:− 1) Radius of…

Q: 6/72 The system is released from rest with the cable taut, and the homogeneous cylinder does not…

A: Mass of the cylinder is: m=7 kg Radius of the cylinder is: r=0.15 m Angle of the slope is: θ=20°…

Q: The cantilever beam shown carries a concentrated load, P = 500 N, and a uniform N/m. Determine the…

A: Given data

Q: 15.127 Knowing that at the instant shown rod AB has a constant an- gular velocity of 6 rad/s…

Q: The change of state from a gas to a solid is called _________ and the change is _______

A: Generally the elements transformation follows as gaseous state to liquid state and then liquid to…

Q: Can you please draw Mohr's circle for the solution above?

A: Given that, σx=350 MPaσy=230 MPaτxy=-480 MPa

Q: The solid shaft in (Figure 1) is subjected to a torque, bending moment, and shear force. igure 300…

Q: 2.92 For the object shown in Figure P2.92, calculate SA for neutral stability when submerged. А 80…

A: Dear Students The answer is given below

Q: Consider a 2-meter simply supported beam with a circular cross section. The beam is subjected to a…

A: Given data:- Length of the beam (L)=2 m Force applied at mid-point (F) =1000 N Bending stress(σb)…

Q: The man in the figure draws the rope tied at point A. It pulls with a force of F=150 N. According to…

A: According to the given data in the question F=150N From the A to B We need to find The Moment of…

Q: why does the highlighted parts become 0?

A: Given Data: ∬CST→ dA+∭CVB→ρ dV=∂∂t∭CVV→ (ρ dV)+∬CSV→(ρV→.dA→) dA Neglect friction and gravitational…

Q: A 20-lb sphere A is held at the 68° angle shown and released. It strikes the 11-lb sphere B. The…

A: The mass of sphere A is ma=20 lb. The mass of sphere B is mb=11 lb. The coefficient of restitution…

Q: During the execution of a nonflow process by a system, the work per degree temperature increase…

Q: A gear reduction unit uses the countershaft shown in the figure. Gear A receives power from another…

A: Pressure angle ϕ=20oTransmitted force FA=11400 NDiameter of shaft dshaft=52 mm

Q: - As the hydraulic cylinder elongates, it raises pin B of the mechanism shown below. For the…

Concept explainers

Slope and Deflection

The slope in a deflected beam is described as an angle in radians made by the tangent of the section with the original axis of the beam. The deflection at any point on the axis of the beam is defined as the lateral displacement of the point before and after loading.

Question

answer must not be in x10 whatever but just inches as the question asks

Use Castigliano's theorem to determine the magnitude of deflection at midspan for the solid steel shaft shown in the figure, where a =
3 in, b = 7 in, da = 1.125 in, db = 1.875 in, and w=160 lbf/in.
da
7
ka
db
W
b
da
a →
The magnitude of deflection at the mid-span of the beam is 0.016265
in.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: Given

VIEW

Step 2: Calculation of deflection at mid-span

VIEW

Solution

VIEW

Step by step

Solved in 3 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

A simple beam with an overhang is subjected to d point load P = 6kN. If the maximum allowable deflect ion at point C is 0.5 mm, select the lightest W360 section from Table F-l{b) that can be used for the beam. Assume that L = 3 m and ignore the distributed weight of the beam.
-5 Calen1ate the deflections S 3a nd
An object of weight Wis dropped onto the midpoint of a simple beam AB from a height h (see figure). The beam has a rectangular cross section of area A. Assuming that h is very large compared to the deflection of the beam when the weight PFis applied statically, obtain a formula for the maximum bending stress crniilx in the beam due to the falling weight.
-10 The simple beam AB shown in the figure supports two equal concentrated loads P: one acting downward and the other upward. Determine the angle of rotation A at the left-hand end, the deflection 1under the downward load, and the deflection 2 at the midpoint of the beam.
A symmetric beam A BCD with overhangs at both ends supports a uniform load of intensity q (see figure). Determine the deflection SDat the end of the overhang. (Obtain the solution by using the modified form of Castiglianos theorem.)
The cantilever beam ACB shown in the figure supports a uniform load of intensity q throughout its length. The beam has moments of inertia I2and IYin parts AC and CB, respectively. Using the method of superposition, determine the deflection SBat the free end due to the uniform load. Determine the ratio r of the deflection 6Bto the deflection 3Xat the free end of a prismatic cantilever with moment of inertia /] carrying the same load. Plot a graph of the deflection ratio r versus the ratio 12 //t of the moments of inertia. (Let 7, tlxvary from I to 5.)
A simple beam with a W 10 x 30 wide-flange cross section supports a uniform load of intensity q = 3.0 kips/ft on a span of length L = 12 ft (sec figure). The dimensions of the cross section are q = 10.5 in., b = 5.81 in., t1= 0.510 in., and fw = 0.300 in. Calculate the maximum shear stress tjuly on cross section A—A located at distance d = 2.5 ft from the end of the beam. Calculate the shear stress rat point Bon the cross section. Point B is located at a distance a = 1.5 in. from the edge of the lower flange.
The cantilever beam ACB shown in the figure has moments of inertia /, and I{in parts AC and CB, respectively. Using the method of superposition, determine the deflection 8Bat the free end due to the load P. Determine the ratio r of the deflection 8Bto the deflection S:at the free end of a prismatic cantilever with moment of inertia /] carrying the same load. Plot a graph of the deflection ratio r versus the ratio 12 //L of the moments of inertia. (Let /, II- vary from I to 5.)
Compound beam ABC is loaded by point load P = 1.5 kips at distance 2aB from point A and a triangularly distributed load on segment BC with peak intensity qü= 0.5 kips/ft. If length a = 5 ft and length/) = 10 ft, find the deflection at B and rotation at A. Assume that £ = 29,000 ksi and / = 53.8 in4.
Copper beam AB has circular cross section with a radius of 0.25 in. and length L = 3 ft. The beam is subjected to a uniformly distributed load w = 3.5 lb/ft. Calculate the required load P at joint B so that the total deflection at joint B is zero. Assume that£ = 16,000 ksi.
The tapered cantilever beam AB shown in the figure has a thin-walled, hollow circular cross sections of constant thickness t. The diameters at the ends A and B are dAand dB= 2dA, respectively. Thus, the diameter d and moment of inertia / at distance x from the free end are, respectively, in which IAis the moment of inertia at end A of the beam. Determine the equation of the deflection curve and the deflection 8 Aat the free end of the beam due to the load P.
-3 The deflection curve for a simple beam AB (see figure) is given by v=q0x360LEI(7L410L2x2+3x4) Describe the load acting on the beam.