Deeper Elasticity Closure Scans

Young Stress Force Closure Three-Row Scan

Young modulus closes strain to stress and then stress to force.

Young modulus closes strain to stress and then stress to force. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Young modulus closes a strain-to-stress-to-force chain

First multiply modulus 12 Pa by strain 1 over 2 to get stress 6 Pa. Then multiply by area 2 square meters to get force 12 N. The accepted bit stays pinned to the cited sources.

σ=Eϵ=12 Pa×12=6 Pa,F=σA=12 N,accepted=1\sigma=E\epsilon=12\ \text{Pa}\times\frac{1}{2}=6\ \text{Pa},\quad F=\sigma A=12\ \text{N},\quad \text{accepted}=1
Young chain closure rowStress, strain, modulus, area, and force close together.forceareaoriginal lengthextensionforce=12 Narea=2 m^2stress=6 PaoriginalLength=6 mextension=3 mstrain=1/2stressSource=boundstrainSource=boundmodulus=12 PaacceptedBit=1 bit

Young modulus closes a strain-to-stress-to-force chain

First multiply modulus 15 Pa by strain 1 over 3 to get stress 5 Pa. Then multiply by area 4 square meters to get force 20 N. The accepted bit stays pinned to the cited sources.

σ=Eϵ=15 Pa×13=5 Pa,F=σA=20 N,accepted=1\sigma=E\epsilon=15\ \text{Pa}\times\frac{1}{3}=5\ \text{Pa},\quad F=\sigma A=20\ \text{N},\quad \text{accepted}=1
Young chain closure rowStress, strain, modulus, area, and force close together.forceareaoriginal lengthextensionforce=20 Narea=4 m^2stress=5 PaoriginalLength=9 mextension=3 mstrain=1/3stressSource=boundstrainSource=boundmodulus=15 PaacceptedBit=1 bit

Young modulus closes a strain-to-stress-to-force chain

First multiply modulus 20 Pa by strain 1 over 4 to get stress 5 Pa. Then multiply by area 6 square meters to get force 30 N. The accepted bit stays pinned to the cited sources.

σ=Eϵ=20 Pa×14=5 Pa,F=σA=30 N,accepted=1\sigma=E\epsilon=20\ \text{Pa}\times\frac{1}{4}=5\ \text{Pa},\quad F=\sigma A=30\ \text{N},\quad \text{accepted}=1
Young chain closure rowStress, strain, modulus, area, and force close together.forceareaoriginal lengthextensionforce=30 Narea=6 m^2stress=5 PaoriginalLength=12 mextension=3 mstrain=1/4stressSource=boundstrainSource=boundmodulus=20 PaacceptedBit=1 bit