Question

A three-point bending test was performed on an aluminum oxide specimen having a circular cross section of radius 6.7 mm; the specimen fractured at a load of 2710 N when the distance between support points was 41 mm. Another test is to be performed on a specimen of this same material, but one that has a square cross section of 19 mm in length on each edge. At what load would you expect this specimen to fracture if the support point separation is maintained at 41 mm?

Answer 1

at load 13114.85 N beam fail

Step-by-step explanation:

given data

radius r = 6.7 mm

load = 2710 N

distance = 41 mm

length = 19 mm

to find out

At what load we expect this specimen to fracture

solution

we will first flexural strength that is

flexural strength = load × distance / πr³

flexural strength = 2710 × 41 ×
`10^(-3)` / π(6.7 ×
`10^(-3)`)³

flexural strength = 117.592 MPa

we know that for cross section specimen

flexural strength = 3load × distance / 2bd²

put here these value

117.592 ×
`10^(6)` N/m² = 3 load × 41 ×
`10^(-3)` / ( 2 × (19×
`10^(-3)`)³)

load = 117.592 ×
`10^(6)` × ( 2 × (19×
`10^(-3)`)³) / ( 3 × 41 ×
`10^(-3)` )

load = 13114.85 N

so at load 13114.85 N beam fail