A beam of length /= 1m, which is clamped at both ends, is modelled using four flexural elements. The first modeshape of the beam is described by:20.5443.0451.0000.0000.544- 3.045Note that Y₁ = ₁=Y₁ = =0 due to the boundary conditions. Recalling that displacement of a flexural element is given by:0y=S₁₂(x) y₂ +S₂(x) @ + S₂(x) y₂ + S₂(x) O111/22where the shape functions are given by:2$, (x) = 1 - 3 ( - ) ²+ ² ( ² ) ³*+2x3$₂(x)=x- 2 + ² + + ²2L L²x$₂(x) = ³ ( 7 ) * - 2 ( ² ) ³+2 x35(x) = -1/ 2 + + 20S₂(x)LL²Find the displacement of the first modeshape at position x=//8. Express your answer to three decimal places and do not include units in your answer.

Answered: Image /qna-images/answer/0f036cd2-8870-4a22-99e3-fc4f22b5be25.jpg

A beam of length /= 1m, which is clamped at both ends, is modelled using four flexural elements. The first modeshape of the beam is described by: O e O 0.544 3.045 1.000 0.000 0.544 -3.045 Note that Y₁ = ₁=Y₁ == 0 due to the boundary conditions. Recalling that displacement of a flexural element is given by: 1 1 5 5 y=S₂(x) y₂ +S₂(x) + S₂(x) y₂ + ₂(x) ₂ O 1 2 where the shape functions are given by: $₁(x) = 1-3 ( ² ) ² + 2 (²) ² S₂(x)=x-2-² +²2 L L2 $₂(x) = 3 ( ² ) ² - ² (+) ² x² x3 + S₂(x)=-I L² Find the displacement of the first modeshape at position x=//8. Express your answer to three decimal places and do not include units in your answer.

A beam of length /= 1m, which is clamped at both ends, is modelled using four flexural elements. The first modeshape of the beam is described by: O e O 0.544 3.045 1.000 0.000 0.544 -3.045 Note that Y₁ = ₁=Y₁ == 0 due to the boundary conditions. Recalling that displacement of a flexural element is given by: 1 1 5 5 y=S₂(x) y₂ +S₂(x) + S₂(x) y₂ + ₂(x) ₂ O 1 2 where the shape functions are given by: $₁(x) = 1-3 ( ² ) ² + 2 (²) ² S₂(x)=x-2-² +²2 L L2 $₂(x) = 3 ( ² ) ² - ² (+) ² x² x3 + S₂(x)=-I L² Find the displacement of the first modeshape at position x=//8. Express your answer to three decimal places and do not include units in your answer.

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

The value of P = 90kN
Elementary beam theory predicts that the axial bending stress ox in a prismatic beam is given by: ox = (M.I,M,L)y+(M,I.-M.I.) (1,1₂-13/2) where My and M₂ are bending moments applied to a cross-section, and where ly, lz and lyz are second moments of area in the usual notation (Oxyz is a Cartesian coordinate system in which the x axis corresponds to the centroidal axis of the beam). (iii) A Z--section beam has the cross-section shown overleaf (see Figure QB2). The second moments of area of the section about the y and z axes are given as;; ly = 1.12x106mm² and I₂ = 2.87x106 mm4. Show that lyz = 1.35x106 mm² (use the parallel axis theorem). 100 60 10 y -10 10 60 Figure QB2 N (iv) Bending moments Mz = 2.0 kNm and My = 0 kNm act on a cross- -section of the beam of part (iii). Obtain an expression for the bending stress and sketch the orientation of the neutral axis with reference to the y and z axes. What is the maximum tensile value of the axial bending stress and where does it occur?
The beam shown below is suspended from two steel rods as shown and is initially horizontal. The midpoint B of the beam is deflected 15 mm downward by force Q. The steel used for the rods has properties E = 200 GPa and σ = 275 MPa, determinea. the required maximum value of Q.b. the deformation of rod AD.c. the deformation of rod CE.
If you know that the line of influence of the reaction force of the joint of the serration in the figure below lies along the member A To bring the truss into equilibrium under the action of force B, find its amount and the reaction of the joint CA .C at a point NΚ10 in vertical
the forces on the gusset plate of a joint in a bridge truss act as shown. shown. Determine the values of P and F to maintain equilibrium of the joint ж 1000 в b to 300016 Jir Fine
A 25mm diameter pin at B connects the crank mechanism loaded as shown in the figure. 500KN 200mm 100mm 45° B What is the value of the horizontal component of P in KN?
A torque of 500 NMm is applied to the circular beam of variable radius given in the figure in the direction shown at point C. Find the support reactions at A and B points.
The frame given in the figure below has three degrees of freedom in C (1,2,3) and three degrees of freedom in B (4,5,6) .In Figure 1:Open the vertical deformation at node C and apply force F and close the other degrees of freedom.Now , If we separate the CD column and the BC beamAccording to the stiffness method What is the status of the forces and moment on the CD in C? In other words, what is the ratio of forces R1 F R3 R4 R5 R6 Apply to CD column in C? And what is the position of the forces and anchors on BC in B and C? In other words, what is the ratio of forces R1 F R3 R4 R5 R6 Applied to BC beams in C and B? In Figure 2:Open the rotation at node C and insert the momentM and close the other degrees of freedom.Now , If we separate the CD column and the BC beamAccording to the stiffness method What is the status of the forces and moment on the CD in C? In other words, what is the ratio of forces R1 R2 M R4 R5 R6 Apply to CD column in C? And what is the position of the forces and…
3. Rigid member ABD is connected to elastic member CDE as shown. For the given loading, what are the vertical displacements of points A and E? A 20KN dimensions in meters B rigid I ст 0.4 E 0.2 5kN E=7oGPa A=100mm²
A cantilever beam is free of support at point A and is clamped at the point B, as shown in the Figure Q4 below. Calculate the support reaction force and moment for the non-uniformly distributed load, where w =74 N/m and L = 6 m. The downward direction is denoted as positive direction in force and the anti- clockwise direction is defined as positve in moment. For all numerical answers, answer to within 3 decimal places. A v y -L- Figure Q4: A cantilever beam under non-uniformly distributed load
A rectangular tetrahedron has six sides of length 9 cm. If a force of 600 N is applied along edge BC as As shown, determine the moment of the 600-N force about edge OA. A B 600 N
2. For the beams shown in figures, determine the displacements and the slopes at the nodes, the forces in each element, and the reactions. I kip 4 20 ft 3 m L 2 W L B 2 20 ft 10 kN 20 kN m W 17 L 3 m B E = 30 x 106 psi I = 100 in C E = 210 GPa /= 4 x 104 m²