50 kN 6.25 kN/m By В 2,5 m 2.5 m 4 m
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A: FH=ρghA=103×9.81×14×35×2×23×5×2=994.08 KnFY=ρgV¯=103×9.81×14×8×8+23×5×2×8=9312.96 Kn
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A: FH=ρghA =103×9.81×14+35×2×23×5×2 =994.08 KN
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- In the figure, rigid bar ABC is supported by axial member (1), which has a cross-sectional area of 400 mm², an elastic modulus of E = 70 GPa, and a coefficient of thermal expansion of α = 22.5 × 10-6 /°C. The temperature rises 56°C causing deformation at pt. B. Determine the deflection at pt. C? A 1.75 m D (1) B 3.75 m 1.25 mThe 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.EXAMPLE 4.2 The rigid bar BDE is supported by two links AB and CD. Link AB is made of aluminum (E = 70 GPa) and has a cross-sectional area of 500 mm²; link CD is made of steel (E = 200 GPa) and has a cross-sectional area of 600 mm?. For the 30-kN force shown, determine the deflection (a) of B, (b) of D, (c) of E. %3D 0.4 m 0.3 m 30 kN D E -0.4 m 0.2 m
- 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…A beam is clamped at point A and is simply supported at point B, as shown in Fig. 2b. It is subjected to a point load and a moment at the free end. Applying Castigliano's Theorem, predict the support reactions at point A and B. El is constant. P Mo A B- L Fig. 2bReactions have been calculated for the beam AB shown in the figure. The shear force at location X (4m to the right of A) is most nearly equal to 6kN 3kN/m A i B VA = 8.4kN Vg = 9.6kN 4m 2m 4m 2m 2m
- Beam AD is supported by a rollers at B and C that are equidistant form the ends, as shown in Fig. P 1.4-14. The beam supports a uniformly distributed downward load of intensity wo (force per unit length) along its entire length. (a) Determine an expression for the location a of the two supports that will minimize the maximum bending moment Mmax in the beam. (b) Also determine an expression for the value of Mmax.A rigid beam BC is suspended by rods AB and CD as shown in the figure. Rod AB is made in from aluminum while rod CD is made from steel. Determine the location/placement of the 75kN concentrated load within the beam BC such that the rigid beam BC will remain horizontal after deflection. Determine the axial deformation of rods AB and CD.2 Find the support reactions in the beam ABC shown in Fig. P.15.2 using the principle of virtual work. Ans. RA=(W+2wL)/4, Rc=(3W+2wL)/4.
- The rigid bar BDE is supported by two links AB and CD. Link AB is made of aluminum (E = 70 GPa) and has a cross-sectional area of 500 mm^2; link CD is made of steel (E = 200 GPa) and has a cross-sectional area of 600 mm^2. For the 30 kN force shown, determine the deflection of B and E, respectively. 0.4 m 0.3 m B A 0.2 m OC -0.4 m 30 kN EDevelop the flexibility matrix for the beams with respect to the co-ordinates shown in figure. 21 2m 1 I 2The propped cantilever beam shown below has a length of 12 meters and is supported by a roller at A and a fixed support at B. The beam has a modulus of elasticity of E = 200 GPa and a constant moment of inertia | = 255(106) mm4. If the beam is subjected to a uniform distributed load of w = 15 kN/m, determine the following using the CONJUGATE BEAM METHOD: 1. Reactions at the supports A and B. 2. Slope at the free end. 3. Maximum deflection.