Properties Of Metals Stress And Strain Practice Questions

Consider the fillet-welded lap joint shown in the figure (Not to scale). The length of the weld shown in the effective length. The welded surface meet at right angle. The weld size is $8 \mathrm{~mm}$ , and the permissible stress in the weld is $120 \mathrm{MPa}$ . What is the safe load $P$ (in $\mathrm{kN}$ , rounded off to one decimal place) that can be transmitted by this welded joint ?

Consider two linearly elastic rods HI and IJ, each of length b, as shown in the figure. The rods are co-linear, and confined between two fixed supports at H and J. Both the rods are initially stress free. The coefficient of linear thermal expansion is $\alpha$ for both the rods. The temperature of the rod IJ is raised by $\Delta T$ , whereas the temperature of rod HI remains unchanged. An external horizontal force P is now applied at node I. It is given that $\alpha ={10^{-6} } {\circ} C^{-1},\Delta T=50^{\circ}C,b = 2 m, AE = 10^6N.$ . The axial rigidities of the rods HI and IJ are 2AE and AE, respectively. To make the axial force in rod HI equal to zero, the value of the external force P (in N) is _________. (round off to the nearest integer)

For a linear elastic and isotropic material, the correct relationship among Young's modulus of elasticity ( $E$ ), Poisson's ratio ( $v$ ), and shear modulus ( $G$ ) is

A square plate O-P-Q-R of a linear elastic material with sides 1.0 m is loaded in a state of plane stress. Under a given stress condition, the plate deforms to a new configuration O-P'-Q'-R' as shown in the figure (not to scale). Under the given deformation, the edges of the plate remain straight. The horizontal displacement of the point (0.5 m, 0.5 m) in the plate O-P-Q-R (in mm,round off to one decimal place) is ________

Strain hardening of structural steel means

The state of stress represented by Mohr's circle shown in the figure is

The total stress paths corresponding to different loading conditions, for a soil specimen under the isotropically consolidated stress state (O), are shown below: The correct match between the stress paths and the listed loading conditions, is

A rigid, uniform, weightless, horizontal bar is connected to three vertical members P, Q and R as shown in the figure. All three members have identical axial stiffness of 10 kN/mm. The lower ends of bars P and R rest on a rigid horizontal surface. When NO laod is applied, a gap of 2 mm exist between the lower end of the bar Q and the rigid horizontal surface. When a vertical load W is placed on the horizontal bar in the downward direction, the bar still remains horizontal and gets displayed by 5 mm in the vertically downward direction. The magnitude of the load W (in kN, round off to the nearst integer), is ______

An isolated concrete pavement slab of length L is resting on a frictionless base. The temperature of the top and bottom fibre of the slab are $T_t \; and \; T_b$ , respectively. Given: the coefficient of thermal expansion $=\alpha$ and the elastic modulus =E. Assuming $T_t \gt T_b$ and the unit weight of concrete as zero, the maximum thermal stress is calculated as

An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal strain in the plane of maximum shear strain is

A plate in equilibrium is subjected to uniform stresses along its edges with magnitude $\sigma_{xx}$ = 30 MPa and $\sigma_{yy}$ = 50 MPa as shown in the figure. The Young's modulus of the material is $2 \times 10^{11} N/m^{2}$ and the Poisson's ratio is 0.3. If $\sigma_{zz}$ is negligibly small and assumed to be zero, then the strain $\varepsilon _{zz}$ is

An elastic bar of length L, uniform cross sectional area A, coefficient of thermal expansion $\alpha$ , and Young's modulus E is fixed at the two ends. The temperature of the bar is increased by T, resulting in an axial stress $\sigma$ . Keeping all other parameters unchanged, if the length of the bar is doubled, the axial stress would be

Consider the stepped bar made with a linear elastic material and subjected to an axial load of 1 kN, as shown in the figure. Segments 1 and 2 have cross-sectional are of $100mm^{2}$ and $60mm^{2}$ , Young's modulus of $2 \times 10^{5}$ MPa and $3 \times 10^{5}$ MPa, and length of 400mm and 900mm, respectively. The strain energy (in N-mm, up to one decimal place) in the bar due to the axial load is __________

A 2 m long, axially loaded mild steel rod of 8 mm diameter exhibits the load-displacement $(P-\delta )$ behavior as shown in the figure. Assume the yield stress of steel as 250 Mpa. The complementary energy (in N-mm) stored in the bar up to its linear elastic behavior will be____

In a material under a state of plane strain, a 10x10 mm square centered at a point gets deformed as shown in the figure. If the Shear strain $\gamma _{xy}$ at this point is expressed as 0.001k(in rad),the value of k is

An elastic isotropic body is in a hydrostatic state of stress as shown in the figure. For no change in the volume to occur, what should be its Poisson's ratio?

A tapered circular rod of diameter varying from 20 mm to 10 mm is connected to another uniform circular rod of diameter 10 mm as shown in the following figure. Both bars are made of same material with the modulus of elasticity, $E=2\times 10^{5}$ MPa. When subjected to a load $P=30\pi kN$ , the deflection at point A is ______ mm.

A box of weight 100 kN shown in the figure is to be lifted without swinging. If all forces are coplanar, the magnitude and direction ( $\theta$ ) of the force (F) with respect to x-axis should be

The values of axial stress ( $\sigma$ ) in kN/ $m^{2}$ , bending moment (M) in kNm, and shear force (V) in kN acting at point P for the arrangement shown in the figure are respectively