problem 1a plane stress element is subjected to

Question

Problem 1:

A plane stress element is subjected to stress components

σ_x = 50 MP_a, σ_y = -10 MP_a, and "τ_xy = 40 MP_a.

1) Draw the Mohr's circle for this stress state.

2) Deterrnine the principal stresses and the angle of the principal direction to the x-axis.

3) Determine the maximum shear stress.

Problem 2:

A simpie be beam subjected to a concentrated moment M_o, force P and a distributed load q
1) Determine the reaction forces at two ends (point A and B).

2) Draw the shear-force and bending moment diagram. Label values at all key points and the maximum. Label each section as constant, linear, quadratic, etc.

3) Determine the maximum shear stress τ_max and maximum bending stress σ_max in the cross-seaction, of the beam.

Problem 3:

A steel column (BD) is used to support a RIGID beam AC(length = 2m)that holds an object weight W. The steel column (E = 200GP_a) has a square cross section of 40 mm x 400 mm  length of L = 2m  

Design 1(top): the column is pinned to the beam and the ground with an additional pinng at the middle.

Design II (bottom): the column is fixed at both ends

Deterrnine the buckling load (WI and W2) in "Design 1" and "Design 2". Which design can support larger load?

 

Problem 4:

A Steel cantilever beam AB is built in to the wall at me end A(fixed) and fixed and supported by a copper wire at end B. The beam is subjected to a concentrated force P=10 KN and a distributed force q = 2 KN/m

Steel Beam AB: Length L = 4 m with a rectangular cross section of hieght 20 cm x width 10 cm

Copper wire BD: Length h = 1m with a circular cross section of diameter d = 5mm

Is this system determinate or indeterminate?

Determine the deflection δ_B of the beam at the end B.

Problem 5:

A circular shaft AB has a diameter of d =0.1 m. The total length of the bar is 2m. The shear modulus G = 90GP_a

the shaft is fixed against rotation at both ends and subjected to TWO torques: T_o at point D) and 2T₀ at the middle point C (see Figure). Torque T_o = 5 Kn -m

Determine the angle of rotation at the middle point C and reaction torque at end B.