Shearing Force and Bending Moment:

Problem 1

Determine the resultant internal loadings acting on the cross section at B of the pipe shown in Fig. (a) The pipe has a mass of 2 kg/m and is subjected to both a vertical force of 50 N and a couple moment of 70 N.m at its end A. It is fixed to the wall at C.

Problem 2

A girder has a uniform T cross-section with flange 250 mm x 50 mm and web 220 mm x 50 mm. At a certain section of the girder there is a shear force of 360 kN.

What are the shear-stress values where the web and the flange of the section meet?

Problem 3

A steel beam with yield strength, σ_yeid = 300 MN/m² is under a stress state as follows:

σ_x = 30 MN/m², σ_y = 150 MN/m², τ_xy = 45 MN/m²

Using the Mohr's circle method, determine the following:

a) The principal normal stresses and the maximum shear stress

b) Sketch a diagram the orientation of the planes of the principal normal stresses and maximum shear stress relative to the original stress ax and σ_y The normal and shear stresses on a plane 30° counterclockwise from the horizontal plane where the 150 MN/m² stress is acting. Under this stress state, what is the safety factors using the Tresca failure theory, the Rankine failure theory and the Von Mises Theory?

Problem 4

A steel bar of circular section 160 mm in diameter is to be used as a column with both of its end pin jointed.

a) If the stress limit is 240 MN/m² and the modulus of elasticity of steel is 2x10¹¹ N/m², calculate the safe load if the length of the column is 8 m with a safety factor of 1.75?

b) If the column is changed from a square to a triangular section with sides of equal lengths and with the same cross-sectional area, calculate the safe load for a length of 8 m and safety factor of 1.75.