Home work 3
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1) The document discusses equations for calculating strain (¦Å) based on load (¦Ò), temperature change (¦¤T), and material properties like modulus of elasticity (E) and coefficient of thermal expansion (¦Á). 2) It provides equations for calculating total strain, stress, and coefficients for composite materials made of two materials with different properties oriented in two directions. 3) The key equations show that the coefficient of thermal expansion for the composite (¦Á1) is the volume fraction-weighted average of the coefficients of the two materials, and similarly for the stress in the second direction (¦Á2).
Home work 3
- 1. Home work (3): ¦¤L= ¦Å L0 + B¦¤m+¦Á¦¤T Hook¡¯s law: 1-according to load (¦Ò): ¦Ò = E ¦Åm 2-according to temp change ¦¤T: ¦Åt = ¦Á . ¦¤T Total strain is ¦Å =¦Åm+¦Åt =¦Ò/E + ¦Á . ¦¤T For direction (1): ¦Å1=¦Åf=¦Åm ¦Åf=¦Òf/Ef+¦Áf.¦¤T ¦Ò1 ¦Åm=¦Òm/Em +¦Ám.¦¤T ¦Òf=Ef(¦Åf-¦Áf T) ¦Òm=Em(¦Åm-¦Ám.T) ¦Ò1=Vf ¦Òf + Vm ¦Òm ¦Ò1=E1(¦Å1-¦Á1 ¦¤T) ¦Ò1=Vf Ef (¦Åf-¦Áf¦¤ T)+Vm Em (¦Åm-¦Ám.¦¤T) by sub with ¦Ò1 E1( ¦Å1-¦Á1 ¦¤T)= Vf Ef (¦Åf-¦Áf¦¤ T)+Vm Em (¦Åm-¦Ám.¦¤T) We have: ¦Å1=¦Åf=¦Åm We can get: ¦Á1 E1 = Vf Ef ¦Áf + Vm Em ¦Ám
- 2. for direction 2: ¦Ò2 ¦Ò2=¦Òm=¦Òf ¦Å2=¦Åf Vf+¦Åm Vm ¦Å= ¦Ò/E + ¦Á . ¦¤T ¦Ò2/E2+¦Á2 ¦¤T= (¦Òf/Ef+¦Áf ¦¤T)Vf+(¦Òm/Em+¦Ám ¦¤T) Vm by solve the last eguation: ¦Á2= ¦Áf Vf +¦Ám Vm