Bar BC in the figure has length L, constant cross sectional area A, and is composed of a homogeneous material with modulus E. The bar is fixed between walls at B (x=0) and C (x = L). The bar is subjected to a variable distributed load per unit length, oriented in the direction indicated in the figure. The magnitude of the distributed load, p(x)=bx, linearly increases from B to C, with a known value for the constant parameter b. Note that b has dimensions [Nm2], so that p(x) has the desired dimensions [Nm].
You will use the force method, taking the wall at B as the redundant support, to solve this SI problem.
The KNOWN problem parameters are L[m], A[m2], E[Pa], and b[Nm2].
1) Obtain a symbolic expression for the axial force resultant along the bar, N(x), in terms of x, b, and of the unknown redundant reaction RxB (enter this as R_B):
N(x)=
2) Obtain a symbolic expression for the axial strain in the bar, ϵa(x) in terms of x, b, E, A, and of the unknown redundant reaction RxB (enter this as R_B):
ϵa(x)=
3) Obtain the redundant reaction, RxB in terms of b and L:
RxB=
4) Obtain a symbolic expression for the axial strain in the bar, ϵa(x) in terms of x, and of the known problem parameters b, E, L and A:
ϵa(x)=
5) Obtain expressions for the axial strain at the two ends of the bar (in terms of the known problem parameters b, E, L and A), and for the position x0 along the bar where the axial strain goes to zero (ϵa(x0)=0), (in terms of L):
ϵa(x=0)=
unanswered
ϵa(x=L)=
unanswered
ϵa(x0)=0atx0=
6) Obtain a symbolic expression for the displacement field, ux(x), in terms of x, and of the known problem parameters b, E, L and A:
ux(x)=
7) Obtain a symbolic expression for the position where the magnitude of the displacement ux is maximum (in terms of L). You might want to use the strain field along the bar for guidance.
xmax=
8) Obtain a symbolic expression for the maximum magnitude (absolute value) of displacement along the bar, umax=|ux|max, in terms of the known problem parameters b, E, L and A:
umax=
0 answers