QuestionA frame as shown in figure 4 is fixed at node 1 and 4 carries a uniformlydistributed load of 84 kN/m on member 1 and a concentrated load of 60 kN onmember 3. Using the stiffness method, determine(a) the rotations at node 2 and displacement at node 3,(b)(c)(d)reacting forces at supports,internal forces of all members, anddraw the deflected shape of the frame, shear force and bendingmoment diagrams. Show the importance values in the diagrams.Given, the modulus of elasticity, E of 200 kN/mm², moment of inertia of thesection, / of 3.55 x 10⁰ mm4 and cross-sectional area, A of 4560 mm² for allmembers.84 kN/m5m232Figure 42.5 m60 KN32.5 mt5m

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Question A frame as shown in figure 4 is fixed at node 1 and 4 carries a uniformly distributed load of 84 kN/m on member 1 and a concentrated load of 60 kN on member 3. Using the stiffness method, determine (a) the rotations at node 2 and displacement at node 3, (b) reacting forces at supports, (c) internal forces of all members, and (d) draw the deflected shape of the frame, shear force and bending moment diagrams. Show the importance values in the diagrams. Given, the modulus of elasticity, E of 200 kN/mm², moment of inertia of the section, / of 3.55 x 109 mm4 and cross-sectional area, A of 4560 mm² for all members. 84 kN/m 5m 2 3 2 Figure 4 2.5 m 60 KN 3 2.5 m t 5m

Question A frame as shown in figure 4 is fixed at node 1 and 4 carries a uniformly distributed load of 84 kN/m on member 1 and a concentrated load of 60 kN on member 3. Using the stiffness method, determine (a) the rotations at node 2 and displacement at node 3, (b) reacting forces at supports, (c) internal forces of all members, and (d) draw the deflected shape of the frame, shear force and bending moment diagrams. Show the importance values in the diagrams. Given, the modulus of elasticity, E of 200 kN/mm², moment of inertia of the section, / of 3.55 x 109 mm4 and cross-sectional area, A of 4560 mm² for all members. 84 kN/m 5m 2 3 2 Figure 4 2.5 m 60 KN 3 2.5 m t 5m

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Matrix Algebra for Structural analysis

Structural analysis is a process in which the effects of different loads and internal forces, acting on structures and their elements are determined. This method of analysis is effective in detecting the failure loads of the structural elements and the design can be altered before commencing the construction process, which ensures proper strength and safety of the structures.

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Step 1: Given that

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Step 2: Fixed end moments

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Step 3: Slope Deflection equations and final end moments

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Step 4: Support reactions

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Step 6: Shear force diagram & bending moment diagram

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1)
The pin-jointed frame in the figure below has members of cross-sectional area A=1200mm² and young modulus of elasticity of 200.5 GPa. If a vertical concentrated load of 1200KN (downward) and horizontal force of 800KN (to the right) are applied at Point D. Determine: a. The vertical displacement at D in mm. b. The horizontal displacement at D in mm. c. The stress of AD due to actual loads in kN. d. The stress of AB due to horizontal unit load. e. The stress of BD due to vertical unit load. 4m B 3m C 3m F E
The rigid beam BC shown in the figure is supported by rods (1) and (2) that have cross-sectional areas of 190 mm2 and 290 mm2, respectively. A uniformly distributed load of w= 12 kN/m is applied on the rigid beam as shown in the figure. Assume L= 3 m, a= 1.7 m, length of rods= 2.1 m and E= 57 GPa. Determine the force in rod (1)? Determine the force in rod (2)? Determine the normal stress in rod (1)? Determine the strain in rod (1)? Determine the deformation in rod (1)? In mm Determine the deformation in rod (2)?in mm
The two sub questions and question g as well :
Replace the loading by an equivalent resultant force and couple moment acting at point 0. Solution Strategy:1. Break the distributed load into “primal” geometric shapes. This problem lends itself to analysis in 3 primal shapes.2. The areas below the load profiles will tell you the magnitudes of the equivalent concentrated loads.3. The position of the individual concentrated loads resulting from breaking up the given load profile will be located at the centroid of each primal.4. Once you have the equivalent concentrated loads and positions for the three primals you can find the resultant force and moment about ? in one of two ways:a. Find a single equivalent force and position (like you did for 11-W) and then relocate this single force to ?? using the techniques from topic 10.b. Use the techniques from topic 10 directly on the three equivalent concentrated loads you found in steps 2 & 3.
For the beam and loading shown, (a) Use discontinuity functions to write the expression for w(x). Include the beam reactions in this expression. (b) Integrate w(x) twice to determine V(x) and M(x). (c) Use V(x) and M(x) to plot the shear-force and bending-moment diagrams. Let a = 3.0 m, b = 1 m, WA = 18 kN/m, and wg = 45 kN/m. Label all significant points on each diagram and identify the maximum shear force and bending moment along with their respective locations. Clearly differentiate straight-line and curved portions of the diagrams. Note that answers may be positive or negative. Here, "maximum" refers to the largest magnitude value, but you should enter your shear force and bending moment with the correct sign, using the sign convention presented in Section 7.2 of the textbook. If the magnitudes of the largest positive and largest negative values are the same, enter a positive number. WB "| WA X C a Answer: Vmax Mmax KN kN.m B b