a. To determine the tensile stresses at yield and at fracture, we need to know the cross-sectional area of the rebar. Let's assume that the cross-sectional area of the rebar is 0.785 square inches (which is the cross-sectional area for a No. 10 steel rebar according to some sources).
The tensile stress at yield is calculated as the yield load divided by the cross-sectional area:
Stress at yield = Yield load / Cross-sectional area = 41,600 lb / 0.785 sq in = 53,011 psi
The tensile stress at fracture is calculated as the fracture load divided by the cross-sectional area:
Stress at fracture = Fracture load / Cross-sectional area = 48,300 lb / 0.785 sq in = 61,508 psi
b. To estimate how much increase in load is required to cause a 1% deformation in the rebar, we need to know the original length of the rebar and the amount of deformation that corresponds to a 1% strain. Let's assume that the original length of the rebar is 12 feet (144 inches) and that a 1% strain corresponds to a deformation of 1.44 inches (which is the amount of deformation for a 12-foot length of rebar subjected to a 1% strain).
To calculate the increase in load required to cause a 1% deformation, we can use the following formula:
Increase in load = Cross-sectional area x Strain x Modulus of elasticity
where the modulus of elasticity for steel is typically around 29,000,000 psi.
Plugging in the values, we get:
Increase in load = 0.785 sq in x 1.44 in / 144 in x 29,000,000 psi = 625.4 lb
Therefore, an increase in load of about 625 lb would be required to cause a 1% deformation in the rebar.