Question

Consider the following beam loaded by a triangular load as shown in figure 1 and having the cross section shown in figure 2. P 40mm A L Figure 1 B 4mm Figure 2 5mm 50 mm For the considered beam, use P = 150 N, L = 1 m, the modulus of elasticity E = 200 GPa and the Poisson coefficient \(\nu = 0.33\). For the T beam, you may use \(\alpha = \frac{A_c}{A_{web}}\), where \(A_c\) is the total cross section area and \(A_{web}\) is the area of the web of the beam. a) Using Castigliano theorem, compute the reaction at the roller B, then find the rest of the reactions. Do not neglect the energy of the shear stresses. b) Using \(R_{Ay} = 60N\), \(R_B = 15 N\) and \(M_A = 10 N.m\), find the slope at point B using Castigliano theorem.

          Consider the following beam loaded by a triangular load as shown in figure 1 and having the
cross section shown in figure 2.
P
40mm
A
L
Figure 1
B
4mm
Figure 2
5mm
50 mm
For the considered beam, use P = 150 N, L = 1 m, the modulus of elasticity E = 200 GPa and the
Poisson coefficient \(\nu = 0.33\).
For the T beam, you may use \(\alpha = \frac{A_c}{A_{web}}\), where \(A_c\) is the total cross section area and \(A_{web}\) is
the area of the web of the beam.
a) Using Castigliano theorem, compute the reaction at the roller B, then find the rest of the
reactions. Do not neglect the energy of the shear stresses.
b) Using \(R_{Ay} = 60N\), \(R_B = 15 N\) and \(M_A = 10 N.m\), find the slope at point B using
Castigliano theorem.

Consider the following beam loaded by a triangular load as shown in figure 1 and having the
cross section shown in figure 2.
P
40mm
A
L
Figure 1
B
4mm
Figure 2
5mm
50 mm
For the considered beam, use P = 150 N, L = 1 m, the modulus of elasticity E = 200 GPa and the
Poisson coefficient ν = 0.33.
For the T beam, you may use α = (Ac)/(Aweb), where Ac is the total cross section area and Aweb is
the area of the web of the beam.
a) Using Castigliano theorem, compute the reaction at the roller B, then find the rest of the
reactions. Do not neglect the energy of the shear stresses.
b) Using RAy = 60N, RB = 15 N and MA = 10 N.m, find the slope at point B using
Castigliano theorem.

Added by Melissa J.

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