A 6m long cantilever beam 250mm x 600mm carries a uniformly distributed dead load (beam weight included) of 5 kN/m throughout the length and a concentrated live load of 18 kN at the free end. To prevent excessive deflection of the beam, it is pre-tensioned with 12mm strands causing a final prestress force of 540 kN. 1. Determine the resulting stress at the bottom fiber at the free end if the center of gravity of the strands coincide the centroid of the section. 2. Determine the resulting stress at the top fiber at the free end if the center of gravity of the strands is at 100mm above the neutral axis of the beam. 3. Determine the eccentricity of the prestress force at the fixed end such that the resulting stress at the top fiber of the beam at the fixed end is zero.
A 6m long cantilever beam 250mm x 600mm carries a uniformly
distributed dead load (beam weight included) of 5 kN/m throughout the
length and a concentrated live load of 18 kN at the free end. To prevent
excessive deflection of the beam, it is pre-tensioned with 12mm
strands causing a final prestress force of 540 kN.
1. Determine the resulting stress at the bottom fiber at the free end if
the center of gravity of the strands coincide the centroid of the
section.
2. Determine the resulting stress at the top fiber at the free end if the
center of gravity of the strands is at 100mm above the neutral axis of
the beam.
3. Determine the eccentricity of the prestress force at the fixed end
such that the resulting stress at the top fiber of the beam at the
fixed end is zero.
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