Bestend Properties is refurbishing an old hospital that was built in the early 1950s. The building’s main structure is a steel frame. The company’s structural engineers are trying to determine the strength of the existing floor beams by loading them up and measuring the deflection, which is given by the formula:
E = 5wL4/384Iy
where:
E is Young’s Modulus of elasticity (strength of the material)
w is the measured uniformly distributed load on the beam
I is the moment of inertia of the beam (a constant due to the cross-sectional shape )
L is the measured span of the beam
y is the deflection of the loaded beam.
After the on-site testing was done, it was discovered that some of the measuring equipment was wrongly calibrated. The errors that were discovered were as follows:
The span L was 5% too long.
The load w was 3% too low.
Using your knowledge of binomial theory, produce a formula to show the net percentage effect of these calibration errors on the value of E (Young’s Modulus).