Cantilever beam under a concentrated load. One end is fixed. Solve for the deflection and stress...
Cantilever beam under a concentrated load. One end is fixed. Solve for the deflection and stress of the cantilever.
y= 1/EI [-1/6Fx^3 + 1/2FL^2x - 1/3FL^3]
E Modulus of Elasticity 70 GPa
I Second Moment of Inertia (bh^3)/12
Length 0.55m
Height 0.0127m
Thickness 0.0635m
Load m=4.53kg applied 0.0325m away from the free end
and gravity = 9.81m/s^2
Homework Answers
summary-
maximum stress induced = 13.47*106 N/m2.
maximum deflection = -6.05*10-2 mm.
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Cantilever beam under a concentrated load. One end is fixed.
Solve for the deflection and stress...
A cantilever beam of length L and constant EI carries a concentrated load P at a...
A cantilever beam of length L and constant EI carries a
concentrated load P at a distance of L/4 from the free end. Use any
method that you chose to develop an expression for the deflection
of the free end. VEI = ?
Loading Loading Function wwx) Shear V /w(xdx Moment M-Vax 1/4 M = M-a) V-M, M-M V-a) N-P) 03 V- M- (3 shop
8. The cantilever beam in Figure Q8 subjects to concentrated loading. The cross section geometry gives...
8. The cantilever beam in Figure Q8 subjects to concentrated loading. The cross section geometry gives the second moment of area / 100 x 10 m. The longitudinal geometry of the beam: a 2 m, b 1 m. The material of the beam: Young's modulus E 200 GPa. The loading: concentrated force P 10 KN. (a) Determine the reactions to the beam at the fixed end. (b) Determine the rotation angle at point x-a (c) (Determine the deflection at the...
The cantilever beam shown is subjected to a concentrated load of P = 34500 lb. The...
The cantilever beam shown is subjected to a concentrated load of P = 34500 lb. The cross-sectional dimensions and the moment of inertia of the W16x31 wide-flange shape are: d = 15.9 in. tw = 0.275 in. be= 5.53 in. tp = 0.440 in. 12 = 375 in 4 Compute the value of the shear stress at point K, located at yk = 2.4 in. above the centroidal axis. bi 11 y 1 K Ук | Ун H Answer: Shear...
The cantilever, shown, has a steel core bonded to a wood casing. If a concentrated load...
The cantilever, shown, has a steel core bonded to a wood casing. If a concentrated load 25 kN is applied at its end, determine the maximum bending stress in the cantilever. Ew = 12 GPa, Es = 200 GPa. 25 kN 3.00 m 200 mm 200 mm Steel 500 mm Wood 500 mm Cross-section of the cantilever For the beam shown, a) Draw the bending moment diagram, b) Determine the maximum normal stress due to bending. 300 N 400 N/m...
2. The governing differential equation that relates the deflection y of a beam to the load w ia w...
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The deflection y, in a simple supported beam with a uniform load q and a tensile load T is given by dx2 El 2EI Where x location along the beam, in meter T-Applied Tension E-Young's Modulus of elasticity of the beam 1= Second moment of inertia of the beam Applied uniform loading (N/m), L- length of the beam in meter Given that T-32 kN, q = 945.7 kN/m, L = 2.0 meter, E = 206 GPa and 1 4.99 x...
(a) A cantilever beam shown in Figure 6 is subjected to a concentrated load P. Deflection...
(a) A cantilever beam shown in Figure 6 is subjected to a concentrated load P. Deflection of the beam at each point can be defined by the following equations: 6EI Pa 6EI F3x-a) for axx<l The following MATLAB code calculates and plots the deflection diagram for a beam with 1-4 m, d1 = 3 m, b = 1 m,E>210 x 10, Pa, 1 = 285 x 10-6 m4 and P = 20 kN. Find at least FOUR errors in the...
For the cantilever beam shown in figure below, we have derived the deflection curve during the...
For the cantilever beam shown in figure below, we have derived the deflection curve during the lecture as: r(z)-하-둬뿌 부] 48 Consider the magnitude of the distributed load q 1 N/m, length of the beam L 1 m, Young's modulus E-200 GPa and the 2nd moment of area about the bending axis is 1 = 250 cm". What is the reaction bending moment at the left end in N.m? Ya 2
Strength of Materials IV 9.2-5 The defiuction curve for a cantilever beam AB (see fgure) is given b 120LEI Describe the load acting on the beam. 2 .3-6 Calculate the maximum deflectio...
Strength of Materials IV
9.2-5 The defiuction curve for a cantilever beam AB (see fgure) is given b 120LEI Describe the load acting on the beam. 2 .3-6 Calculate the maximum deflection dma of a uniformly loaded simple beam if the span length L 5 2.0 m, the intensity of the uniform load g 5 2.0 kN/m, and the maximum bending stress s 5 60 MPa. rn X The cross section of the beam is square, and the material is...
The cantilever beam shown is subjected to a concentrated load of P = 46200 lb. The...
The cantilever beam shown is subjected to a concentrated load of
P = 46200 lb. The cross-sectional dimensions and the
moment of inertia of the W16x40 wide-flange shape are:
d = 16.0 in.
tw = 0.305 in.
bf = 7.00 in.
tf = 0.505 in.
Iz = 518 in.4
Compute the value of the shear stress at point K, located at
yK = 2.4 in. above the centroidal axis.
by P y T tw K Lyk Z d x Ун...
A cantilever beam of length L and constant EI carries a
concentrated load P at a distance of L/4 from the free end. Use any
method that you chose to develop an expression for the deflection
of the free end. VEI = ?
Loading Loading Function wwx) Shear V /w(xdx Moment M-Vax 1/4 M = M-a) V-M, M-M V-a) N-P) 03 V- M- (3 shop
8. The cantilever beam in Figure Q8 subjects to concentrated loading. The cross section geometry gives the second moment of area / 100 x 10 m. The longitudinal geometry of the beam: a 2 m, b 1 m. The material of the beam: Young's modulus E 200 GPa. The loading: concentrated force P 10 KN. (a) Determine the reactions to the beam at the fixed end. (b) Determine the rotation angle at point x-a (c) (Determine the deflection at the...
The cantilever beam shown is subjected to a concentrated load of P = 34500 lb. The cross-sectional dimensions and the moment of inertia of the W16x31 wide-flange shape are: d = 15.9 in. tw = 0.275 in. be= 5.53 in. tp = 0.440 in. 12 = 375 in 4 Compute the value of the shear stress at point K, located at yk = 2.4 in. above the centroidal axis. bi 11 y 1 K Ук | Ун H Answer: Shear...
The cantilever, shown, has a steel core bonded to a wood casing. If a concentrated load 25 kN is applied at its end, determine the maximum bending stress in the cantilever. Ew = 12 GPa, Es = 200 GPa. 25 kN 3.00 m 200 mm 200 mm Steel 500 mm Wood 500 mm Cross-section of the cantilever For the beam shown, a) Draw the bending moment diagram, b) Determine the maximum normal stress due to bending. 300 N 400 N/m...
2. The governing differential equation that relates the deflection y of a beam to the load w ia where both y and w are are functions of r. In the above equation, E is the modulus of elasticity and I is the moment of inertia of the beam. For the beam and loading shown in the figure, first de m, E = 200 GPa, 1 = 100 × 106 mm4 and uo 100 kN/m and determine the maximum deflection. Note...
The deflection y, in a simple supported beam with a uniform load q and a tensile load T is given by dx2 El 2EI Where x location along the beam, in meter T-Applied Tension E-Young's Modulus of elasticity of the beam 1= Second moment of inertia of the beam Applied uniform loading (N/m), L- length of the beam in meter Given that T-32 kN, q = 945.7 kN/m, L = 2.0 meter, E = 206 GPa and 1 4.99 x...
(a) A cantilever beam shown in Figure 6 is subjected to a concentrated load P. Deflection of the beam at each point can be defined by the following equations: 6EI Pa 6EI F3x-a) for axx<l The following MATLAB code calculates and plots the deflection diagram for a beam with 1-4 m, d1 = 3 m, b = 1 m,E>210 x 10, Pa, 1 = 285 x 10-6 m4 and P = 20 kN. Find at least FOUR errors in the...
For the cantilever beam shown in figure below, we have derived the deflection curve during the lecture as: r(z)-하-둬뿌 부] 48 Consider the magnitude of the distributed load q 1 N/m, length of the beam L 1 m, Young's modulus E-200 GPa and the 2nd moment of area about the bending axis is 1 = 250 cm". What is the reaction bending moment at the left end in N.m? Ya 2
Strength of Materials IV
9.2-5 The defiuction curve for a cantilever beam AB (see fgure) is given b 120LEI Describe the load acting on the beam. 2 .3-6 Calculate the maximum deflection dma of a uniformly loaded simple beam if the span length L 5 2.0 m, the intensity of the uniform load g 5 2.0 kN/m, and the maximum bending stress s 5 60 MPa. rn X The cross section of the beam is square, and the material is...
The cantilever beam shown is subjected to a concentrated load of
P = 46200 lb. The cross-sectional dimensions and the
moment of inertia of the W16x40 wide-flange shape are:
d = 16.0 in.
tw = 0.305 in.
bf = 7.00 in.
tf = 0.505 in.
Iz = 518 in.4
Compute the value of the shear stress at point K, located at
yK = 2.4 in. above the centroidal axis.
by P y T tw K Lyk Z d x Ун...
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