Determine the equation of the elastic curve using the coordinate x, and specify the slope at point A and the deflection at point C. EI is constant.
The equation of elastic curve using the coordinate
Answer to Problem 7.1P
The equation of elastic curve is shown below.
The slope at point A is,
The deflection at C is,
Explanation of Solution
Calculation:
The following figure shows the free body diagram of the beam.
Figure-(1)
Write the Equilibrium Equation for the sum of horizontal forces.
Here, horizontal reaction at A is
Write the Equilibrium Equation for the sum of vertical forces.
Here, vertical reactions at point A and B are
Due to symmetry of the beam, the reactions at point A and B will be half of the total load acting on the beam.
Consider the section x-x at distance
Write the Equation for sum of moment about x-x.
Write the differential equation of the elastic curve as shown below.
Substitute
Here,
Calculate the value of
Apply the boundary conditions at the support points.
At
Substitute
Calculate the value of
At
Substitute
Calculate the slope equation.
Substitute
Calculate the deflection equation.
Substitute
Calculate the slope at A.
Substitute
Calculate the deflection at C.
Substitute
Conclusion:
The equation of elastic curve is shown below.
The slope at point A is,
The deflection at C is,
Want to see more full solutions like this?
Chapter 7 Solutions
Structural Analysis (10th Edition)
Additional Engineering Textbook Solutions
Materials for Civil and Construction Engineers (4th Edition)
Foundation Design: Principles and Practices (3rd Edition)
Elementary Surveying (14th Edition)
Elementary Surveying: An Introduction To Geomatics (15th Edition)
Introduction to Java Programming and Data Structures, Comprehensive Version (11th Edition)
- Determine the equations of the elastic curve for the beam using the x1 and x2 coordinates. Specify the beam’s maximum deflection. EI is constant.arrow_forwardDetermine the equations of the elastic curve, v(x), for the beam using the x1 and x2 coordinates. Specify the beam’s maximum deflection. EI is constant.arrow_forwardDetermine the equations for the elastic curve for the beam using the x-coordinate. Specify the slope at A, slope at B, deflection at the center of the beam (x = L/2) and the maximum deflection. EI is constant.arrow_forward
- For the beam and loading shown determine (a) the equation of the elastic curve, (b) the deflection at the left end of the beam. Assume that EI is constant for the beam. w(x)=w₁ x ³/L³ Wo T L Barrow_forwardProb 4. The simply supported steel beam (E triangular load as shown below. (El is constant). If/when you use integration you must solve for constants & simplify = 29,000 ksi), has a rectangular cross section as shown, and supports the Derive the bending moment equation M(x), for the first half of the beam. Show your work Derive the slope equation, 0 (x). Show your work Derive the deflection equation, A(x). Show your work Sketch the general shape of the deflection line. Determine the maximum deflection Amax of the beam Hint: The maximum deflection occurs when 0(x) = 0, which happens at the point where M (x) = Mmax Beam's X-section 10 k/ft 10 in ל ץל77 -12 ft - 12 ft 4 inarrow_forwardDetermine the equation of the elastic curve for the beam using the x coordinate that is valid for 0 < x < L. EI is constant.arrow_forward
- Determine the displacement and the rotational at point D, considering that the moment of inertia I=300 in4, the elastic modulus is the same for the section of the beam with a value of E=29000 Ksi. Use Castigliano's method for beams. Point D is half the distance from segment AB. The following figure shows the applied loads, distances, and conditions at the beam supports.arrow_forward3. The shaft is attached to rigid fixed supports at each end. The maximum shear stress will be equal in both segments when the torque T is applied at B Determine the d.. Use 2 decimal places. Use the given sign convention for uniformity. dAn =? dac = 40 mm 0 (+) 1200 mm 800 mmarrow_forwarddetermine the equations of the elastic curve using the coordinates and specify the slope at B and deflection at c. EI is constantarrow_forward
- Derive the equation of the elastic curve for the beam using the x coordinate that is valid for ?≤ ?< ?. Specify the slope at A and the beam’s maximum deflection. EI is constant.arrow_forwardDetermine the equation of the elastic curve for the beam using the x coordinate that is valid for 0 < x < L. EI is constant. Also, determine the maximum deflection and rotation at the free end.arrow_forwardDetermine deflection at free end . Given EI=constantarrow_forward
- Structural Analysis (10th Edition)Civil EngineeringISBN:9780134610672Author:Russell C. HibbelerPublisher:PEARSONPrinciples of Foundation Engineering (MindTap Cou...Civil EngineeringISBN:9781337705028Author:Braja M. Das, Nagaratnam SivakuganPublisher:Cengage Learning
- Fundamentals of Structural AnalysisCivil EngineeringISBN:9780073398006Author:Kenneth M. Leet Emeritus, Chia-Ming Uang, Joel LanningPublisher:McGraw-Hill EducationTraffic and Highway EngineeringCivil EngineeringISBN:9781305156241Author:Garber, Nicholas J.Publisher:Cengage Learning