ch. 4 Statically indeterminate

statically indeterminate

• equilibrium equations are not enough to determine the reactions

• need to consider the condition of deformation

compatibility condition

specifies a condition of displacement

express as a load displacement relationship

principle of superposition

the resulting stress or displacement at a point can be found first finding the stress or displacement caused by each load separately, and then adding them algebraically

force method

• based on superposition, we can write compatibility first to solve

• find the displacement caused by each external force plus the displacement caused by the redundant support to write the compatibility first

thermal stresses and strains

change in temperature can cause a material to change dimensions when unstretched

increase in temperature

expansion

decrease in temperature

contraction

α

coefficient of thermal expansion

total strains

strains caused by temperature changes and by applied loads are essentially independent

thermal stresses

if free to expand then no stress arises due to temperature change but in a statically indeterminate member, thermal displacements will be constrained by the support

axial loading

∑δ = 0

δ1 = δ2