41. Rivets and bolts subjected to both shear stress (τ_{vf, cal}) and axial tensile stress (σ_{tf, cal}) shall be so proportioned that the stresses do not exceed the respective allowable stresses τ_vf and σ_tf and the value of
    

    		τvf, cal	+	σtf, cal
    		τvf		σtf

    
    does not exceed

1. 1. 1.0

   
   
   

   2. 1.2

   
   
   

   3. 1.4

   
   
   

   4. 1.8

   
   
   

---

1. View Hint View Answer Discuss in Forum

   1.4

   Correct Option: C

   1.4

---

42. A steel strip of length, L = 200 mm is fixed at end A and rests at B on a vertical spring of stiffness, k = 2 N/mm. The steel strip is 5 mm wide and 10 mm thick. A vertical load, P = 50 N is applied at B, as shown in the figure. Considering E = 200 GPa, the force (in N) developed in the spring is____________
    

1. 1. 3

   
   
   

   2. 12

   
   
   

   3. 6

   
   
   

   4. 9

   
   
   

---

1. View Hint View Answer Discuss in Forum

   
   

   K =	F
   	δ

   
   

   K =	R
   	δ

   
   

   ⇒ δ =	R
   	K

   
   For cantilever,
   

   δ =	(p - R)L3	=	R
   	3EI		k

   
   
   ⇒ R = 3N

   Correct Option: A

   
   

   K =	F
   	δ

   
   

   K =	R
   	δ

   
   

   ⇒ δ =	R
   	K

   
   For cantilever,
   

   δ =	(p - R)L3	=	R
   	3EI		k

   
   
   ⇒ R = 3N

---

---

43. Cross-section of a column consisting of two steel strips, each of thickness t and width b is shown in the figure below. The critical loads of the column with perfect bond and without bond between the strips are P and P₀, respectively. The ration P/P₀ is
    

1. 1. 2

   
   
   

   2. 4

   
   
   

   3. 6

   
   
   

   4. 8

   
   
   

---

1. View Hint View Answer Discuss in Forum

   P α 2 E I
   

   α z ×	1	× bt3
   	12

   
   P α E l₁
   

   α E ×	1	× b(2t)3
   	12

   
   

   ∴	P	= 4
   	P0

   Correct Option: B

   P α 2 E I
   

   α z ×	1	× bt3
   	12

   
   P α E l₁
   

   α E ×	1	× b(2t)3
   	12

   
   

   ∴	P	= 4
   	P0

---

44. A mild steel specimen is under uni-axial tensile stress. Young’s modulus and yield stress for mild steel are 2 × 105 MPa respectively. The maximum amount of strain energy per unit volume that can be stored in this specimen without permanent set is

1. 1. 156 Nmm/mm³

   
   
   

   2. 15.6 Nmm/mm³

   
   
   

   3. 1.56 Nmm/mm³

   
   
   

   4. 0.156 Nmm/mm³

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Max strain energy unit volume
   

   =	σy2
   	2E

   
   

   =	250 × 106	= 156250 Nm/m3
   	2 × 2 × 1011

   
   = 0.156 Nmm/mm³

   Correct Option: D

   Max strain energy unit volume
   

   =	σy2
   	2E

   
   

   =	250 × 106	= 156250 Nm/m3
   	2 × 2 × 1011

   
   = 0.156 Nmm/mm³

---

---

45. The plastic collapse load W_p for the propped cantilever supporting two point loads as shown in figure terms of plastic moment capacity, M_p is given by
    

1. 1. 3 M_p /L

   
   
   

   2. 4 M_p /L

   
   
   

   3. 4 M_p /L

   
   
   

   4. 6 M_p /L

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Max positive moment under load = PL/3
   

   ∴	PL	=	mp + mp	=	4mp
   	3		3		3

   
   

   ∴ P =	4mp
   	L

   Correct Option: B

   Max positive moment under load = PL/3
   

   ∴	PL	=	mp + mp	=	4mp
   	3		3		3

   
   

   ∴ P =	4mp
   	L

---